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:
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)