Is $f(x)=4xe^x$ increasing or decreasing at $x=-2$ ?

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Answer 1 · 2016-01-11T14:13:24

It's decreasing.

In order to know, you calculate the derivative of $f$ and you evaluate it at $-2$ .

By the product rule, $f'(x) = 4e^x + 4xe^x$ .

We now evaluate $f'(2) = 4e^(-2) -8e^(-2) = 4/e^2 - 8/e^2 = -4/e^2 < 0$ becase $e^2 > 0$ . So $f$ is decreasing at $x = -2$ .

Is f(x)=4xe^x f(x)=4xe^x increasing or decreasing at x=-2 x=-2 ?