2.1D Graphing f(x) Given the Graph of f'(x)
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- เผยแพร่เมื่อ 5 ก.ย. 2024
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We are given the graph of f'(x), the derivative. I will show you how to sketch the graph of the original function f(x).
This is so much fun you guys! It's like playing a game.
For weeks, I grappled with understanding these graphs, diligently watching numerous videos that failed to provide clear explanations. Fortunately, after watching your video, I finally grasped the concepts behind these graphs. Thanks a lot 👍.
You are super welcome. Let me send you the link to my full set of calculus videos for easy access.
There’s a lot more where that came from 😎:
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@@MrHelpfulNotHurtful thanks a lot
This was super hard to learn for me, but the table made it super easy, thanks! Coming up clutch for my Calc final. Also think you should've mentioned that when you go from + to - or - to + there'll be a min/max, but you made that clear with ur sketches
You are right. The min/max details is a good connection to make. I will remember that for future videos. Thanks! 😊
AMAZING WONDERFUL REALLY U R THE BEST
Yay!! I appreciate your feedback. 😊
How would you know if f(x) crosses the x axis
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.
Thank you sirr it's very helpful
I really appreciate your feedback! Please tell your class about my channel. th-cam.com/users/MrHelpfulNotHurtfulplaylists?view=50&sort=dd&shelf_id=1&view_as=subscriber
Wow, this is such a great explanation and with so many good examples. "So here we go...."!
Yay! I appreciate your feedback Angieg. ☺
This was a great video. Thank you :)
You are super welcome. I appreciate the feedback. 😊
Thank you this was super helpful!
You are super welcome. Glad to help. 😊
Can you do a video given the second derivative graph and have to draw the function
Making videos by request is a service I reserve for my Patreon supporters. However, I do have a video like the one you requested: th-cam.com/video/VqU7Qm0Ul4k/w-d-xo.html
MrhelpfulNothurtful more like MRHURTFULNOTHELPFUL
😔
Excellent explanation
Thank you so much for the feedback. It means a lot. 😊
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superb explanation
I really appreciate the feedback 😊.
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The way we read f'(x) graph is different from the graph f(x). Based on the given graph f'(x), I see in the interval [-7,10], the function is above zero (y-axis) and f'(x) >0 , which is increasing. I don't see the function goes below the zero at all. How you say the f'(x) is decreasing? I am confused. 😕
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.
I have a test on this today. Lets hope this is helpful🤞
Good luck 🍀
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The same method apply to from f" to f'? Let's say the graph in the video is f" and I want to draw f' is it gonna be the same?
Yes. 😎
Is there a name for this point where cc change? 4:25
It’s called a point of inflection.
It is very helpful
Yay! I appreciate the feedback. 😎
What do we do to find max/min for f graph?
For the f graph, the max and min will just be the highest and lowest point on the graph.
Thank you soooooooo much!!!
You are super welcome!
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Thank you so much!
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Please tell your classmates I’m here 😄.
Thank youuu
Yay! So glad I could help.
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ahhhh I hate graphing these functions
I feel your pain 😭
Bruh got to sleep
😴