Find the intervals on which fx increases given that fx x3

Question

1. Find the interval(s) on which f(x) increases, given that

f(x) = x³ - 12x + 1

2. Find the interval(s) on which f(x) increases, given that

f(X) =- 2x (25x² + 75 + 72)

3. Find the interval(s) on which f(x) increases, given that

f(x) = {5(x² + 25)} / (x² - 25)

4. Find the interval(s) on which f(x) increases, given that

F(x) = (9/4) cos (2x) + (9/2) √3 cos (x)

5. Find f(x), given that

f'(x) = 15 x² - 2

for all x and

f(2) = 41