1. ## Calculus curve sketching

sketch the graph of a function f having given characteristics

f(2) = f(4) = 0
f(3) is defined.
f'(x) < 0 if x < 3
f'(3) does not exist.
f'(x) > 0 if x > 3
f"(x) < 0, x does not equal 3

2. ## Re: Calculus curve sketching

Hey asilverster635.

If you show us what you have tried and any partial attempts you have made, then you will get a more specific and directed answer from other members.

3. ## Re: Calculus curve sketching

i have no idea how to do this type of problem

4. ## Re: Calculus curve sketching

If the derivative doesn't exist at a point it means there is a discontinuity.

If you have a positive derivative it means the function is increasing: if it is negative then it is decreasing.

If f(3) is defined but f'(3) doesn't exist, then it means you have either a discontinuity in the graph or the graph itself has a "kink" in it and isn't smooth (but is still continuous).

If second derivative is increasing then first derivative is increasing: if decreasing then derivative is decreasing.

There are many solutions to this problem graphically and function-wise but they will have the attributes outlined with the above characteristics of derivatives.

5. ## Re: Calculus curve sketching

All of these have a graphical equivalent - for example f(2)=0 means that the graph passes through (0,2). Once you have "translated" them all, you have a description of the graph, so you just need to draw it.

- Hollywood

6. ## Re: Calculus curve sketching

Originally Posted by chiro
If the derivative doesn't exist at a point it means there is a discontinuity.
Technically not correct - the graph could have a "kink" like the function f(x)=|x| at x=0.

Originally Posted by chiro
If second derivative is increasing then first derivative is increasing: if decreasing then derivative is decreasing.
It's probably better to say that if the second derivative is negative, then the function is concave down. And also (though it's not needed for this problem) if the second derivative is positive, then the function is concave up.

- Hollywood

thanks guys

8. ## Re: Calculus curve sketching

Originally Posted by hollywood
the graph could have a "kink" like the function f(x)=|x| at x=0.
A better word would be "corner". I don't know of any mathematical term for it.