What is the extreme f(x)=4xe^{-3x} ?

The extreme f(x)=4xe^{-3x} is Maximum(1/3 , 4/(3e))

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extreme f(x)=4xe^{-3x}

extreme points

f (x) = 4 x e^{- 3 x}

Maximum (\frac{1}{3}, \frac{4}{3 e})

Solution steps

Find the critical points:

x = \frac{1}{3}

Domain of

4 x e^{- 3 x} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < \frac{1}{3},

Decreasing

: \frac{1}{3} < x < \infty

Plug the extreme point

x = \frac{1}{3}

into

4 x e^{- 3 x} \Rightarrow y = \frac{4}{3 e}

Maximum (\frac{1}{3}, \frac{4}{3 e})

f (x) = y (3 x - 5)

f (x) = 3 x - 7

f (x) = 2 x - 24 x^{\frac{1}{3}}

f (x) = - \frac{1}{6000} x + \frac{85}{6}

f (x) = 3 x - 5

What is the extreme f(x)=4xe^{-3x} ?
The extreme f(x)=4xe^{-3x} is Maximum(1/3 , 4/(3e))