Question

Determine all of the relative extreme values of the function f(x) = x^3 - 2x^2 + x + 1

Answer 1

A. The absolute extreme values occur at x = 0 and 1.
B. The absolute extreme values occur at x = 1/3 and 1.
C. The absolute extreme value occurs at x = 0.
D. There are no relative extreme values.

Answer 2

Calculus?

Answer 3

yes

Answer 4

Find f'(x), set it to zero and solve. That will give the location of the relative maximums/minimums. Calculate f"(x) and substitute the x values that found in the previous step. If the second derivative is positive, there is a minimum at that value of x; if negative, it's a maximum. If it is zero, there is usually a point of inflection, but the test is inconclusive.

By the way, this function has no absolute maximum or minimum; a third degree polynomial has end behavior that goes to positive and negative infinity.

Answer 5

ok

Answer 6

i got B is it correct?

Answer 7

yep. you are correct.