What is the extreme f(x)=-(5x+3)e^{-2x} ?

The extreme f(x)=-(5x+3)e^{-2x} is Minimum(-1/10 ,-(5e^{1/5})/2)

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extreme f(x)=-(5x+3)e^{-2x}

extreme points

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

Minimum (- \frac{1}{10}, - \frac{5 e ^{\frac{1}{5}}}{2})

Solution steps

Find the critical points:

x = - \frac{1}{10}

Domain of

- (5 x + 3) e^{- 2 x} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{10},

Increasing

: - \frac{1}{10} < x < \infty

Plug the extreme point

x = - \frac{1}{10}

into

- (5 x + 3) e^{- 2 x} \Rightarrow y = - \frac{5 e ^{\frac{1}{5}}}{2}

Minimum (- \frac{1}{10}, - \frac{5 e ^{\frac{1}{5}}}{2})

\frac{x ^{2}}{x ^{2} + 2 x - 15}

f (x, y) = - x^{2} + 5 y^{2} + 10 x - 10 y - 28

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

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

f (x) = 120 x - 0.4 x^{4} + 1000

What is the extreme f(x)=-(5x+3)e^{-2x} ?
The extreme f(x)=-(5x+3)e^{-2x} is Minimum(-1/10 ,-(5e^{1/5})/2)