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Popular >

extreme f(x)=xe-4x^2

Solution

extreme points

f (x) = x e - 4 x^{2}

Solution

Maximum (\frac{e}{8}, \frac{e ^{2}}{16})

Solution steps

f^{'} (x) = e - 8 x

Find intervals:

Increasing

: - \infty < x < \frac{e}{8},

Decreasing

: \frac{e}{8} < x < \infty

Plug

x = \frac{e}{8}

into

x e - 4 x^{2} : \frac{e ^{2}}{16}

Maximum (\frac{e}{8}, \frac{e ^{2}}{16})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=xe-4x^2 ?
The extreme f(x)=xe-4x^2 is Maximum(e/8 ,(e^2)/(16))