Derivative Applications - Free Formula Sheet: bit.ly/4eV6r1b Access The Full Video on Patreon: www.patreon.com/MathScienceTutor Direct Link - Questions 13 thru 31: bit.ly/2Y3Aem5
Thanks! I am a retired chemistry and physics teacher helping a Calc AB student. Your videos refreshed my skills with very clear examples and warnings of common mistakes. BTW, I tutored Organic for several decades.
Thank you for existing. My teacher doesn’t teach and just assigns problems and trying to teach myself is really rough. Your videos make everything so much simpler.
Our professors simply link us to youtubers & other professors' videos and then assigns homework generated & graded by third-party websites. I'm beginning to wonder if these professors are worth the salaries they're making.
@@beatriceines3456 Yeah, that's the flip side of it, there are plenty of teachers that do so much and truly change a student's life by being such a beneficial influence, and their income doesn't come close to reflecting that :( Some of my high school teachers really went above and beyond to make the world a better place in any way they could, but they probably get paid around the same as my current Professor Redirect. He was a friendly guy the one time I've talked with him, but he's never taught our class a single thing. If I didn't need a degree to prove my education, I'd be able to do the exact same thing I'm currently doing, but for free, and that's what really gets to me. With the k-12 teachers you mentioned, there's no way I'd have learned anything without (most of) them. Those are the real MVPs.
1:29 1.) Find two numbers whose sum is 60 and whose product is a maximum. 7:38 2.) Find two numbers whose difference is 40 and whose product is a minimum. What is the value of the minimum product? 13:09 3.) Find two positive numbers whose product is 400 and whose sum is a minimum. 16:46 4.) Find a positive number where the sun of that number and it's reciprocal is a minimum. 20:42 5.) Find the dimensions of a rectangle with a perimeter of 200 ft with an area as large as possible. 23:09 6.) A farmer has 600ft of fencing and wants to create a rectangular field along a river. He needs no fence along the river itself. What are the dimensions of the field that has the longest area? 27:01 7.) A farmer wishes to create a rectangular field along a river with an area of 10,000 ft^2. What are the dimensions of the field that will require the least amount of fencing? 30:52 8.) A farmer uses 1600 ft of fencing to enclose a rectangular area which will be divided into 3 pens. What is the maximum total area of the 3 pens that he can enclose with the limited amount of fencing that he has available? 34:48 9.) Find the point on the line y= 3x+5 that is closest to the origin. 39:53 10.) Find the point on the line y=4-x that is closest to the point (7,6). 48:27 11.) Find the point on the curve y=6x^2-x^3+10 that has the highest slope. Calculate the maximum value of the slope. 53:33 12.) A rectangle is inscribed in a semicircle with a radius of 10 cm. What are the dimensions of the rectangle that will maximize its area? Calculate the maximum area.
My biggest problem in my calculus 1 course is the algebra, and finding ways to simplify or rationalize problems so that the formulas and methods given apply. My professor always shortcuts her algebra by two or three steps, making her work hard to follow. Thank you for showing every step along the way to the solution. Your videos mean the world to me this semester, and I'm sure I'll be back next semester for calculus 2!
@@shubhamkumar-vx4ld Please do refrain from using « you people » in the future, and a lot of people take calculus 1 and even calc 2 in high school. I’m also in college and almost every very persons I know that are going in a scientific major took calculus 1 during their senior year in high school.
@@MeroVPN i have deleted it thanks anyway we don't have to learn it was just me 😭 not able to get it as I was not preparing for school but for some competition to prestigious gov college
Holy cow. I’ve been crying over stress about these problems since my professor teaches so poorly, and I cannot tell you how grateful I am for this video of yours! I’m appalled at how quick I got the hang of the subject. Thank you!!
JG is the BEST! HIs explanations are clear, easier to understand, and concised. Whatever I search, JG covers. Great job JG. I shall buy Calculus hoodie to support you! Thank you for saving my neck over and over again.
timestamp Sum & Product of 2 numbers 1:30 - 20:41 Fencing 20:42 - 34:49 Distance btw point & line 34:50 - 53:33 Rectangle inscribed in semicircle 53:34 - end
@@omarDababa23 oh i thought you are in college because everbody here in the comments are talking about calc subject so i think they are studying for their college exams
you literally explained optimization way better and easier than my Calculus SI leader!! Definitely gonna book mark this video so I can watch all of it whenever the semester is over.
Hi! I just wanted to thank you because you are singlehandedly getting me through school. I am a Mechanical Engineering major and you explain things twenty times better than any professor I have ever had. Just wanted to thank you so much because you are the reason for my good grades.
38:53 This is one hell of a solution, but still I learned another approach. But if you want a less complicated solution, remember that when dealing with distance on a cartesian plane problems, the square of the distance formula is also maximized and minimized. Basically, if the distance formula is D=√(Xsub2-Xsub1)²+(Ysub2-Ysub1)², then the square of it is D²=(Xsub2-Xsub1)²+(Ysub2-Ysub1)². Always remember than you can always find the derivative of this function even if it's in its squared form. Now, we need at least 1 set of point and express this function into one variable in order to differentiate. Remember that the other set of point is given at the origin-(0,0). So, D²=(Xsub2-0)²+(Ysub2-0)² or just basically D²=(X)²+(Y)². The value of Y is already given as Y=3x+5. Substituting this expression into the equation; D² = x² + (3x+5)². Always remember the square of a binomial in the form (a+b)²=a²+2ab+b², that just means you need to take the square of the first term, multiply the first and second term and multiply the result to 2, and square the second term. We will get: D² = x² + 9x² + 30x + 25 Simplying this equation; D² = 10x² + 30x + 25 Now, this looks like a quadratic equation right? But don't let the function deceive you, take note that you'll be DIFFERENTIATING the equation. So, dD²/dx= 20x+30 and don't forget to equate to 0 to find the maximum/minimum value. Solving for x, x = -30/20 or simplified; -3/2. Then the rest will be easy.
I have a nelson calculus and vectors textbook which I think is standard in Ontario grade 12 calc courses, and at least 3 of these problems were taken from the textbook. This has helped me tremendously because instead of looking at the answers in the textbook, I have mr organic chemistry tutor show me how it’s done.
Here's a trick at 37:00. You don't have to find the derivative of the whole radical because the minimum of what's inside the radical is the same thing as the whole function. So you can just find the derivative of x^2+(3x+5)^2 which is 20x+30, and you get -3/2 for x as well
People say your phones Rot your brain but I’m learning more about these calculus problems from this guy than my actual teacher, thank you for existing my guy.
I dont who you are or where you live, i just pray from my heart that you get the best of your life. Thank you for existing and making our graduation lives easier🖤
In question 11, I think the critical points found as zero of the first derivative should be evaluated with the second derivative to classify the points where the curve will have local minimum and a local maximum and not the zeros of the second derivative function rather(those are used for checking intervals of concavity). Thank you sir
I have been watching this guy my whole first year of college and he really is the goat. Thank you so much. with out your videos I won't have understood anything in my classes so thank you are always having a video for whatever I look up. keep up the good work.
You have made it possible for me to obtain Computer Science degree, I always recommend your content, and the best thing is that the University introduced you to me.
throughout my academic and college life I never heard of constraint equation or objective equation I just recently learned it in this video never knew there was such a thing. Massive thanks to you
Professor Organic Chemistry Tutor, thank you for a lengthy and outstanding video/lecture on Optimization Problems in Calculus One. Although word problems are problematic, I found these problems/examples real helpful in learning this topic. This is an error free video/lecture on RU-vid TV with the Organic Chemistry Tutor.
Thank you for effective presentation that provides a concise Introduction to the theory and brief descriptiom of the technique. Presentation is simply breathtaking because it assumes no previously knowledge of the subject and will be for benefit.
I follow another playlist for math, although I love that guy, but I do not understand a word he says. You, on the other hand, got such a talent for teaching. I always come out of your videos understanding everything fully.
2:35 Constraint equation = fixed value Objective function 2:38 = what we are trying to maximize (find first derivative, set it equal to zero, solve x or y
This has been very helpful for me to solve optimization problems thank you. One thing I don't understand is why is it that whether or not we are finding the max or the min we just set the derivative to zero and find the variable? For example in the first problem we find the maximum product but what if the question had asked for the minimum product? Then using this method would not have given us the correct answer.
Related rates and optimization problems are definitely the hardest questions in year 1 calculus. If you understand this stuff, it's smooth sailing from here :)
my school really likes third derivatives of transcendental functions in their tests. I shudder to think how optimization tests we will have will look like
Thanks for the videos, but a small suggestion, please put the questions a little lower so it doesn't get covered by the title of the video when paused in fullscreen.
For those one, who used to think or not about this question in 1:29 like this: "if we can find max of 2 number whose sum is 60, so can we find min of 2 number whose sum is 60 ?" After take a few min to think, there's no way to figure out, cause the graph of this function just only has max value. It's may useful or not but the lesson is i want to share my perspective on a problem to you in any kind of work.
48:23 We can achieve the same results with less work like so: #1 realize a line-k that is perpendicular to line-y and passes through (7, 6) P(x1, y1) will be the closest point, intersection of line-k and line-y #2 calculate the general form of the line-k k = ax + b a = - 1/(y-line a) b = 6 - a * 7 I hope the numbers are not confusing #3 find P(x1, y1) k = y x1 - 1 = 4 - x1 y1 = 4 - x1
another way to think about question 1 is setting the sum equal to 2 sides of a perimeter of a 4 sided shape. The maximum area will always be a square, therefore the 2 side lengths must be equal
If you think about the last question really, for the greatest product we know the numbers have to be as close to eachother as possible. Now think about only quadrant 1 or quadrant 2 . The numbers would be as close to eachother when they are the same. So we are gonna fit a square in 1/4 of a circle. We know no matter how far we go from the origin, we can only go as far as 10cm, so the diagonal line is 10cm. We can use pythagorean theorem to figure out the sides since a^2 and b^2 are the same. So c^2 would be radius squared, which makes 100=2x^2, x^2 is 50 therefore x= root 50. Now that you know both the sides of the square add your 2 squares together(there is your rectangle) So the height would be root 50, and the bottom would be 2 root 50. What human mind is capable of is insane guys.
Bro my teacher is such garbage. Like rather than going through multiple examples and teaching us how to work these out, he just does like 1 example and wastes all class time doing the math. Like bruh were in calc 3 we all know how to do math just teach us the method. So frustrating. This guy is 100x better teacher
