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

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

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Answer 1 · 2016-11-06T20:21:07

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

1 Answer

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