Consider the function below. f(x) = 9 + 4x^2 − x^4

Question

(a) Find the interval(s) where the function is increasing. (Enter your answer using interval notation.)

Find the interval(s) where the function is decreasing. (Enter your answer using interval notation.)

(b) Find the x-coordinate(s) of any local minima. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Local minima at x = 

 

Find the x-coordinate(s) of any local maxima. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Local maxima at x = 

(c) Find the interval(s) where the graph is concave upward. (Enter your answer using interval notation.)

Find the interval(s) where the graph is concave downward. (Enter your answer using interval notation.)

Find the x-coordinate(s) of any inflection points. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Inflection point(s) at x = 

 

Answer 1

Determine f'(x)

Factor the polynomial and examine intervals with Algebra 2 techniques.