What is the extreme f(x)=4xe^{-0.2x} ?

The extreme f(x)=4xe^{-0.2x} is Maximum(5,(20)/e)

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extreme f(x)=4xe^{-0.2x}

extreme points

f (x) = 4 x e^{- 0.2 x}

Maximum (5, \frac{20}{e})

Solution steps

Find the critical points:

x = 5

Domain of

4 x e^{- 0.2 x} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 5,

Decreasing

: 5 < x < \infty

Plug the extreme point

x = 5

into

4 x e^{- 0.2 x} \Rightarrow y = \frac{20}{e}

Maximum (5, \frac{20}{e})

f (x) = 6

y = x (x + 2)^{2}

- 0.1 t^{2} 0.8 t + 98.8, 0 \leq t \geq 8

f (x) = 4 x^{2} + x y + 252 x + 4 y^{2} - 252 y

f (x) = \frac{t}{1 + t ^{2}}

What is the extreme f(x)=4xe^{-0.2x} ?
The extreme f(x)=4xe^{-0.2x} is Maximum(5,(20)/e)