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Let f(x) = 4x^3 ? 9. Find the open intervals on which f is increasing (decreasin

ID: 2883343 • Letter: L

Question

Let f(x) = 4x^3 ? 9. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). f is increasing on the intervals _____ f is decreasing on the intervals _____ The relative maxima of f occur at x = _____ 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". In the last two, your answer should be a comma separated list of x values or the word "none".

Explanation / Answer

given f(x) = 4x^3 - 9

f'(x) = 12x^2

for crtitcal points f'(x) = 0

12x^2 = 0

x=0

1. f is inceasing for NONE

2. f is decreasing for (-inf , inf )

3. relative maxima NONE

4. relative minma NONE