31) Locate, name, and classify the extrema of the function. Determine intervals which the function is increasing and decreasing

Question

f(x) = -x(x^2 - 2)

32) Determine the end behavior of the function
f(x) = 2x - x^3

Answer 1

#31
since f'(x) = -3x^2+2
the extrema are at x = ±√(2/3)
f' > 0 for -√(2/3) x < √(2/3) so f is decreasing on that interval, and increasing elsewhere.

#32
Since f(x) is odd, and the x^3 coefficient is -1, it rises to the left and drops to the right.