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

1 Answer
evant939012
Apr 5, 2018

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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