# Thread: Extrema & Inflection Points

1. ## Extrema & Inflection Points

The derivative of a function f is given by f '(x)=(x^3-2x)(cos x) for [0,2] (both endpoints are greater than or equal to x).

A) Find the x coordinate of the relative minimum of f(x).
B) Find the x coordinate of the inflection of the graph of f(x).
C) Find the x coordinate of the point at which f(x) attains an absolute maximum.

A) I got sqrt(2).

B) I know that you have to set the second derivative equal to zero. However i don't know how to solve for x is this particular case:
0=(3x^2-2)(cos [x])-(x^3-2x)(sin[x])

C) I don't know how to do this without being given the original function (we haven't started with integration in our class yet so that is not an option)

Please Help

2. Originally Posted by rawkstar
The derivative of a function f is given by f '(x)=(x^3-2x)(cos x) for [0,2] (both endpoints are greater than or equal to x).

A) Find the x coordinate of the relative minimum of f(x).
B) Find the x coordinate of the inflection of the graph of f(x).
C) Find the x coordinate of the point at which f(x) attains an absolute maximum.

A) I got sqrt(2).

B) I know that you have to set the second derivative equal to zero. However i don't know how to solve for x is this particular case:
0=(3x^2-2)(cos [x])-(x^3-2x)(sin[x])

C) I don't know how to do this without being given the original function (we haven't started with integration in our class yet so that is not an option)

Please Help
This particular question is a calculator question from an old AP exam. You're supposed to use your calculator to graph f'(x) and use it's capabilities to answer these questions.

3. ok good because i have no idea how to do this analytically