Is #f(x)=(x-16)(x-12)(x/4+3)# increasing or decreasing at #x=1#?

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Is #f(x)=(x-16)(x-12)(x/4+3)# increasing or decreasing at #x=1#?

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Answer 1 · 2016-01-08T12:37:10

The gradient is negative so the function is decreasing

Explanation:

First expand the expression to simplify it, then differentiate to find the gradient. The gradient is negative if the function is decreasing and positive if it is increasing.
#f(x) = (x-16)(x^2/4 -36) = (x^3/4 -4x^2 - 36x + 576)#
#f'(x) = (3x^2)/4 -8x -36#
#f'(1) = 3/4 - 8 -36 = -43*1/4#

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Is #f(x)=(x-16)(x-12)(x/4+3)# increasing or decreasing at #x=1#?

1 Answer

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