Please help! The only correct answer I got was the last one, 2,-2 For the functi

Question

Please help!

The only correct answer I got was the last one, 2,-2

For the function f(x) = x3 - 12x + 10, find all intervals where the function is increasing: f is increasing on (Give your answer as an interval or a list of intervals, e.g., (-infinity ,8] or (1,5), (7,10).) Similarly, find all intervals where the function is decreasing: f is decreasing on [(-infinity,-2), (-infinity,2) (Give your answer as an interval or a list of intervals, e.g., (-infinity ,8] or (1,5), (7,10) .) Finally, find all critical points in the graph of f(x) critical points: (Enter your X-values as a comma-separated list, or none if there are no critical points.)

Explanation / Answer

f(x) = x^3 - 12x + 10

f ' (x) = 3x^2 - 12

= 3(x^2 - 4)

= 3(x - 2)(x + 2)

a) f is increasing => f'(x) > 0

=> x = (-INF, -2) U (2, INF)

b) f is increasing => f'(x) > 0

=> x = (-2, 2)

c) x = -2, 2

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