Sketching a Function Based on a Derivative Graph, Example 2

[patrickjmt]

if the slope of the tangent line is positive, the derivative is positive. if the slope of the tangent line at a point is negative, the derivative will be negative at that point.

the y value of a function at particular x value does not affect the value of the derivative at that x value.

[capabilites]

in the words of Flula, "who did make you??" you are a genius

[jpmoench]

PATRICK. you've inspired me to help people out with their math issues! i've been helping people on yahoo answer and posting a link to your website so that you can guide them in the future. =)

[ay]

Thanks for teaching these confusing math concepts. They are very helpful.

[patrickjmt]

x^4 looks like x^2. the derivative of x^4 is a cubic. i agree that you might be confused. in that case, maybe you should not think that it is wrong...?

[TRIBALSEEDZ]

You should draw derivatives when the graphs have sharp points and breaks but this video was really helpful.

[patrickjmt]

@FXrubiP videos on it in the ' calculus 2 ' playlist on my channel

[sofiavaldez]

niceee. I never thought of it in this way. I just thought: numbers on x-axis are critical numbers which means there's an extrema there. To figure out which extrema, I would look to the left, if the derivative is below then it's decreasing to the left, and if to the right the graph of derivative is above x-axis then it's increasing.. so then with that I would draw a minimum extremum (a parabola facing up) ...never thought of it in terms of 'y values of derivative represent slope of tangent lines of f'

[patrickjmt]

@pquiba why does it have to be at (0, 0)?

[patrickjmt]

@TheDevilzfriend i am not sure what you mean exactly...

[bubblesnuggles]

So if the graph of the derivative is x^3, then shouldn't the graph of the original function be x^4? You're showing a parabola, which is x^2. Wouldn't that be the graph of the 2nd derivative?

[patrickjmt]

@TheMls1492 nah, i am just a regular dude

[jessylee]

For example 1, f' (x)=0 as x=0, which means the original curve changes concavity as x=0. Therefore the original function you draw is not correct

[kro]

Thank you so much! Very interesting how one can translate graphs...

[theretrogamer]

There's no derivative at a cusp because a tangent line at a cusp does not exist. If you think about it, it is quite impossible to draw a line tangent to a sharp point, thus the slope at the cusps are undefined.

[Chrisymcmb]

Thank you!
Question: Would it also be possible that for the function f(x) in the video example, that the derivative instead also just look like a straight positive linear slope line?

[PureInsanity]

Pat, what about calculus 2's cylindrical shell formula?

[XxMysticxX]

How do you figure out the specific points. I'm trying to do problem number 65 from Calc 7e book. How do you determine the specific points where it crosses and how to make an accurate sketch.

[goncayalcin]

These videos are great, thank you SO much. But I have a question on this one: so the original graph is like a parabola, which means its something along the lines of x^2, but then the derivative looks like a tertiary curve. How is that possible?

[pquiba]

How come the vertex of the graph of f isnt (0, 0)?