What is the extreme f(x)=e^x(15-x^2) ?

The extreme f(x)=e^x(15-x^2) is Minimum(-5,-(10)/(e^5)),Maximum(3,6e^3)

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extreme f(x)=e^x(15-x^2)

extreme points

f (x) = e^{x} (15 - x^{2})

Minimum (- 5, - \frac{10}{e ^{5}}), Maximum (3, 6 e^{3})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 5

into

e^{x} (15 - x^{2}) : - \frac{10}{e ^{5}}

Minimum (- 5, - \frac{10}{e ^{5}})

Plug

x = 3

into

e^{x} (15 - x^{2}) : 6 e^{3}

Maximum (3, 6 e^{3})

Minimum (- 5, - \frac{10}{e ^{5}}), Maximum (3, 6 e^{3})

What is the extreme f(x)=e^x(15-x^2) ?
The extreme f(x)=e^x(15-x^2) is Minimum(-5,-(10)/(e^5)),Maximum(3,6e^3)