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

The extreme f(x)=-(5e^{-x})/(5-3x) is Maximum(2/3 ,-5/(3e^{2/3)})

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

extreme points

f (x) = - \frac{5 e ^{- x}}{5 - 3 x}

Maximum (\frac{2}{3}, - \frac{5}{3 e ^{\frac{2}{3}}})

Solution steps

Find the critical points:

x = \frac{2}{3}

Domain of

- \frac{5 e ^{- x}}{5 - 3 x} : x < \frac{5}{3} or x > \frac{5}{3}

Find intervals:

Increasing

: - \infty < x < \frac{2}{3},

Decreasing

: \frac{2}{3} < x < \frac{5}{3},

Decreasing

: \frac{5}{3} < x < \infty

Plug the extreme point

x = \frac{2}{3}

into

- \frac{5 e ^{- x}}{5 - 3 x} \Rightarrow y = - \frac{5}{3 e ^{\frac{2}{3}}}

Maximum (\frac{2}{3}, - \frac{5}{3 e ^{\frac{2}{3}}})

f (x, y) = 3 x^{2} - 2 x y + y^{2} - 8 y

f (x, y) = x^{2} + y^{2} - 6 y + 9

f (x) = x^{2}, - 1 \leq x \leq 0

3 x^{2} - 5 x + 2

f (x) = x^{4} - 4 x^{3} + 16 x + 4

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