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

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

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Answer 1 · 2018-04-05T04:05:35

Decreasing. Instantaneous rate of change -10

Explanation:

To find if the function is decreasing, we need the first derivative. The easiest way to do this is to expand into the cubic and then use the power rule:

#f(x)=x^3-2x^2-9x+18#

Taking the derivative:

#f'(x)=3x^2-4x-9#

This "function" tells us the slope at x. So, plug in x=1:
#f'(1)=3(1^2)-4(1)-9#
#=3-4-9#
#=-10#

Since #f'(1)# is negative the slope of #f(1)# is negative and hence it is decreasing.

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

1 Answer

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