Is f(x)=(x-2)(x+5)(x-1) increasing or decreasing at x=-1?

1 Answer
Anjali G
Nov 6, 2016

f(x) is decreasing when x=-1

Explanation:

To determine whether f(x) is increasing or decreasing at x=-1, we have to check whether f'(x) is positive or negative at x=-1.

First, find f'(x) using product rule:
f(x) = (x-2)(x+5)(x-1)
f'(x) = cancel((1))(x+5)(x-1) + (x-2)cancel((1))(x-1) + (x-2)(x+5)cancel((1))
f'(x) = 3x^2+4x-13

Next, find f'(-1):
f'(-1)=-14

Since f'(-1) is negative, that means that f(x) is decreasing when x=-1.

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