What is the extreme f(x)=2e^{-x}(x^2-x+1) ?

The extreme f(x)=2e^{-x}(x^2-x+1) is Minimum(1, 2/e),Maximum(2, 6/(e^2))

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extreme f(x)=2e^{-x}(x^2-x+1)

extreme points

f (x) = 2 e^{- x} (x^{2} - x + 1)

Minimum (1, \frac{2}{e}), Maximum (2, \frac{6}{e ^{2}})

Solution steps

Find the critical points:

x = 1, x = 2

Domain of

2 e^{- x} (x^{2} - x + 1) : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug the extreme point

x = 1

into

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

Minimum (1, \frac{2}{e})

Plug the extreme point

x = 2

into

2 e^{- x} (x^{2} - x + 1) \Rightarrow y = \frac{6}{e ^{2}}

Maximum (2, \frac{6}{e ^{2}})

Minimum (1, \frac{2}{e}), Maximum (2, \frac{6}{e ^{2}})

\frac{x}{x ^{2} - 49}

\frac{3 + x}{x - 2}

y = \frac{x + 2}{x ^{2}}

200

f (x) = 33 e^{- 6 x} - 30 e^{- 5 x}

What is the extreme f(x)=2e^{-x}(x^2-x+1) ?
The extreme f(x)=2e^{-x}(x^2-x+1) is Minimum(1, 2/e),Maximum(2, 6/(e^2))