What is the extreme y=(2-3x)/(e^x) ?

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

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extreme y=(2-3x)/(e^x)

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{5}{3}

into

\frac{2 - 3 x}{e ^{x}} : - \frac{3}{e ^{\frac{5}{3}}}

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

mi d p o in t (1, 0.5), (0.5, 2)

a sy m pt o t es f (x) = 25 x^{2} - 14 x - 5 x

in v erse y = - 3 x + 5

d o main 8 - x

in v erse 4 + 3 x

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