Is #f(x)=(x-2)(2x-3)(2x-1)# increasing or decreasing at #x=-2#?

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Is #f(x)=(x-2)(2x-3)(2x-1)# increasing or decreasing at #x=-2#?

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Answer 1 · 2015-12-08T16:04:33

Increasing.

Explanation:

Calculate the first derivative when #x=-2#. If the value is negative, the function is decreasing at that point.If the value is positive, the value is increasing at that point.

First, to avoid doing annoying three-pronged product rule, distribute the binomials.

#f(x)=4x^3-16x^2+19x-6#

#f'(x)=12x^2-32x+19#

#f'(-2)=48+64+19#

#f'(-2)# is positive, so the function is increasing at this point.

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Is #f(x)=(x-2)(2x-3)(2x-1)# increasing or decreasing at #x=-2#?

1 Answer

Explanation:

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