Determine the x-coodinates of all relative maxima (minima)

Question

Let f(x)=4x³+5. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

1. f is increasing on the intervals=

2. f is decreasing on the intervals=

3. the relative maxima of f occur at x=

4. the relative minima of f occur at x=

Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none".

Answer 1

Determine the x-coodinates of all relative maxima (minima)
Let f(x)=4x3+5. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).
1. f is increasing on the intervals= - inf. to 0 and 0 to inf.
2. f is decreasing on the intervals= none
3. the relative maxima of f occur at x=infinity
4. the relative minima of f occur at x= minus infinity