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Popular >

monotone f(x)=xe^{-x^2}

Solution

monotone intervals

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

Solution

Decreasing : - \infty < x < - \frac{1}{2}, Increasing : - \frac{1}{2} < x < \frac{1}{2}, Decreasing : \frac{1}{2} < x < \infty

Solution steps

f^{'} (x) = - e^{- x^{2}} (2 x + 1) (2 x - 1)

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{2},

Increasing

: - \frac{1}{2} < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Decreasing : - \infty < x < - \frac{1}{2}, Increasing : - \frac{1}{2} < x < \frac{1}{2}, Decreasing : \frac{1}{2} < x < \infty

Popular Examples

inflection f(x)=x^4-4x^3+9 inflection points

f (x) = x^{4} - 4 x^{3} + 9

domain of f(x)= 1/(2-3x)domain

f (x) = \frac{1}{2 - 3 x}

inverse of f(x)=\sqrt[3]{x-8}inverse

inverse of f(x)=52.947x^{0.16}inverse

f (x) = 52.947 x^{0.16}

intercepts of f(x)=-(x+1)^2 intercepts

f (x) = - (x + 1)^{2}

Frequently Asked Questions (FAQ)

What is the monotone f(x)=xe^{-x^2} ?
The monotone f(x)=xe^{-x^2} is