What is the extreme e^x(21+9x-x^2) ?

The extreme e^x(21+9x-x^2) is Minimum(-3,-(15)/(e^3)),Maximum(10,11e^{10})

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extreme e^x(21+9x-x^2)

extreme

Minimum (- 3, - \frac{15}{e ^{3}}), Maximum (10, 11 e^{10})

Solution steps

f^{'} (x) = - e^{x} (x + 3) (x - 10)

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 10,

Decreasing

: 10 < x < \infty

Plug

x = - 3

into

e^{x} (21 + 9 x - x^{2}) : - \frac{15}{e ^{3}}

Minimum (- 3, - \frac{15}{e ^{3}})

Plug

x = 10

into

e^{x} (21 + 9 x - x^{2}) : 11 e^{10}

Maximum (10, 11 e^{10})

Minimum (- 3, - \frac{15}{e ^{3}}), Maximum (10, 11 e^{10})

What is the extreme e^x(21+9x-x^2) ?
The extreme e^x(21+9x-x^2) is Minimum(-3,-(15)/(e^3)),Maximum(10,11e^{10})