2.1D Graphing f(x) Given the Graph of f'(x) 

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@@MrHelpfulNotHurtful thanks a lot

You are right. The min/max details is a good connection to make. I will remember that for future videos. Thanks! 😊

Yay! I appreciate your feedback Angieg. ☺

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😔

There is no way to tell if f(x) crosses the x-axis based on the graph of f’(x). In fact, if you take one possible graph of f(x) and shift it up or down, you get another possible graph of f(x). We can only tell the shape of f(x) not the height, so the possible graphs of f(x) will have different x-intercepts.

Making videos by request is a service I reserve for my Patreon supporters. However, I do have a video like the one you requested: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-VqU7Qm0Ul4k.html

It’s all about the relationship between f, f’ and f” given at 0:14. When f’ is above the x-axis like (-7,10) that means f’ is positive. The chart reminds us that when f’ is positive, f is increasing. On the interval (-7, 10) f’ is increasing some of the time and decreasing some of the time. On intervals where f’ is increasing (uphill) , it is ok to say f’ is increasing. However, the chart reminds us that we also know that f is concave up and f” is positive on such intervals. We can get a ton of information from the graph of f’. It’s just a matter of what you are trying to accomplish. For example you could use the graph of f’ to figure out where f is concave up and where it is increasing. If this raises additional questions I will try to answer them 😎.

@@MrHelpfulNotHurtful Thank you for explaining. I wish you have a video explain what happens to f'(x) and f'(x) as x approach to infinity with a given f'(x) graph and a horizontal asymptote.

@@LeNguyen-im8dm Say the f'(x) graph has a horiz asymptote at y=2. So f'(x) approaches 2 as x approaches infinity. Since f'(x) is the slope of f(x), this means the slope of f(x) approaches 2 as x approaches infinity. In other words, if you looked at the far right side of the f(x) graph it would look like a diagonal line with a slope of 2, but really it is approaching an a diagonal asymptote with a slope of 2.

@@MrHelpfulNotHurtful WOW. Thank you for your explanation. I got it.

@@MrHelpfulNotHurtful I got wrong one question on the exam yesterday. Now, I understand what you said,"On the interval (-7, 10) f’ is increasing some of the time and decreasing some of the time." I thought if the f'(x) is above the x-axis, it always increasing.

Good luck 🍀

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Yes. 😎

It’s called a point of inflection.

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Please tell your classmates I’m here 😄.

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For the f graph, the max and min will just be the highest and lowest point on the graph.

😴

I feel your pain 😭