# Extrema & Inflection Points

• Dec 4th 2009, 04:06 PM
rawkstar
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)

• Dec 4th 2009, 04:22 PM
skeeter
Quote:

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)