What is the extreme 10xe^{-2x} ?

The extreme 10xe^{-2x} is Maximum(1/2 , 5/e)

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extreme 10xe^{-2x}

extreme points

10 x e^{- 2 x}

Maximum (\frac{1}{2}, \frac{5}{e})

Solution steps

Find the critical points:

x = \frac{1}{2}

Domain of

10 x e^{- 2 x} : - \infty < x < \infty

Find intervals:

Increasing

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

Decreasing

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

Plug the extreme point

x = \frac{1}{2}

into

10 x e^{- 2 x} \Rightarrow y = \frac{5}{e}

Maximum (\frac{1}{2}, \frac{5}{e})

f (x) = \frac{e ^{x}}{x ^{3}}, x > 0

f (x, y) = ln (y - ∣ x ∣ - 1)

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

f (x) = 7 (x^{2} + 1)^{2} (x - 5)^{3}

f (x) = 9 x^{4} - 4 x^{3}, - 3 \leq x \leq 3