For the function below, determine each of the following. g(x) = 5x^4 + 20x^3 + 13

Question

(a) Find the critical values of g(x). (Enter your answers as a comma-separated list.)

x =

(b) Find the intervals on which g(x) is increasing and the intervals on which g(x) is decreasing. Enter your answers using interval notation.

Increasing:

 

Decreasing:

(c) Find the x-coordinates of all relative extrema on the graph of g(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Relative Maxima:
Relative Minima:

Answer 1

g(x) = 5x⁴ + 20x³ + 13

g'(x) = 20x³ + 60x² = 20x²(x + 3) = 0 when x = 0 or -3

When x < -3, g'(x) < 0. So, g is decreasing

When -3 < x < 0, g'(x) > 0, so g is increasing.

When x > 0, g'(x) < 0, so g is decreasing

Rel max when x = 0

Rel min when x = -3