Question

What is the maximum number of relative extrema contained in the graph of this function?

f(x)=3x^3-x^2+4x-2

Answer 1

There global extrema are at positive and negative infinity -
http://www.wolframalpha.com/input/?i=3x%5E3-x%5E2%2B4x-2

Answer 2

FYI when ever a problem ask you to find max or min, you just derive

Answer 3

and then f(x)=0.
and then find the critical value

Answer 4

Plot f(x) on your graphing calculator or at https://www.desmos.com/calculator
If you don't see any hills and valleys there is no relative extremum.

Or trying solving f'(x) = 0. If there are no real roots then there is no relative extrema.

Answer 5

f'(x) = df/dx

Answer 6

I couldn't find any!

Answer 7

Then that's your answer!