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

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

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

extreme points

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

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}, (- 3, 2) : - 3 < x < 2

Find intervals:

Decreasing

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

Increasing

: - \frac{1}{10} < x < 2

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})

x x - 1

f (x) = x^{3} - 15 x^{2} + 12 x + 7

f (x) = 3 x^{2} - 4 x

f (x, y) = x^{2} + y^{2} + 16

x + 3, 0 \leq x \leq 2

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