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

Quote:

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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

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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.

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