Graphing a Derivative Function Instructor: Christine Breiner View the complete course: ocw.mit.edu/18-01SCF10 License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu
Thanks a lot Madam, I am watching your videos daily and I am proud to say that you put me in time machine and shifted to my first year degree Calculus class in college. My lecturer was also very good in conveying the message, but at that time it was a bit difficult for me to grasp the concept initially but later picked up with confidence. But now it is like standing under a shower of information and I enjoyed soaking to the core. Thanks again Follower from Tamilnadu India
all i can say is that ive been struggling with this for more than 2 lectures, but somehow in 12 minutes of listening to you,i completely understand it! THANK YOU SO MUCH!
Thank you, this is very helpful, but it looks like at the beginning and the end the slope is fairly constant as the line seems pretty straight. I think the beginning and end of the graph of f'(x) should be closer to flat.
Can you demonstrate how to graph the derivatives when there are removable discontinuity (holes in f(x) graph) and non-differentiables (cusp or sharp corner with f(x) graph), maybe using the same graph?
Great video! Only 2 issues I had were: 1) The ends of the graph look like straight lines or constant slope tangents so the derivatives should have actually been closer to constant than continuously increasing/decreasing. 2) The part in the middle actually doesn't make sense to me as a continuously decreasing curve. If it is continuously decreasing then how is there a point where the tangent is zero?
I wish that my math professors in college would have been this explanatory.. I'm serious!! A couple of them went furiously fast because they were either fast talkers or they were full-time at another University and part-time where I was attending college AND OUR CLASS DIDN'T START UNTIL 6:00 P.M. AND WE WERE THERE UNTIL 9:30 SO HE WAS READY TO GO HOME!! ONE OF MY MATH TEACHERS MISSED ONE WEEK BECAUSE HE HAD A DEATH IN THE FAMILY AND THE NEXT WEEK BECAUSE HIS NECK HURT. IT WAS AT THE VERY END OF THE TERM AND OUR CLASS WAS TWO AND A HALF WEEKS BEHIND. WE CAME INTO CLASS AND HAD TO TEST AND THEN THE LAST WEEK AND A HALF OF CLASS RUSHED THROUGH EVERYTHING THAT WE MISSED FOR 2 WEEKS. IT WAS A MESS! WE TOOK OUR FINAL FIVE DAYS AWAY AND IT STILL DIDN'T HELP. I HAD 96.5 BEFORE HE WAS OUT AND THEN AFTER I GOT A 75 ON MY FINAL AND A 70 ON ANOTHER TEST; THE NEXT TWO CHAPTERS WE FLEW THROUGH IN A WEEK THAT HAPPENED TO BE THE MOST DIFFICULT, I ENDED UP WITH AN 89.5. I'M JOKINGLY ASKED HIM IF HE GAVE ANY EXTRA CREDIT OR I COULD WORK ON IT HE TOLD ME "NO". I'M GETTING READY TO GO BACK TO COLLEGE AND FINISH TWO YEARS OF COLLEGE TO BE A MATH TEACHER.. I'VE ALWAYS LOVED MATH. IN GRADE SCHOOL I HAD ALL EXCELLENT MATH TEACHERS EXCEPT FOR ONE, WHO WAS BORING. SHE HAPPENED TO BE MY GEOMETRY TEACHER. ALL OF MY OTHERS WERE GREAT AND I LOVED MATH. THE INSTRUCTORS HELP SO MUCH!!
But this is verging on bollocks! F'(x), the slope of the f(x), to the left is almost constant until it nears the first stationary point, and so f'(x) should be almost horizontal until it nears the first stationary point, and it is nothing like horizontal, it is over 45 degree slope upwards!. The same problem occurs on her depiction of the derivative on the right side of the graph. And the question at the end was almost meaningless.
Great video, however just be careful about how long the gradient being = 0 lasts for. Her graph is technically wrong as there should be a break in the middle of the 'w' as the gradient stays 0 for a while. But in terms of teaching this, fantastic.
