What is the extreme f(x)=e^x(24-x^2) ?

The extreme f(x)=e^x(24-x^2) is Minimum(-6,-(12)/(e^6)),Maximum(4,8e^4)

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extreme f(x)=e^x(24-x^2)

extreme points

f (x) = e^{x} (24 - x^{2})

Minimum (- 6, - \frac{12}{e ^{6}}), Maximum (4, 8 e^{4})

Solution steps

f^{'} (x) = - e^{x} (x - 4) (x + 6)

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 6

into

e^{x} (24 - x^{2}) : - \frac{12}{e ^{6}}

Minimum (- 6, - \frac{12}{e ^{6}})

Plug

x = 4

into

e^{x} (24 - x^{2}) : 8 e^{4}

Maximum (4, 8 e^{4})

Minimum (- 6, - \frac{12}{e ^{6}}), Maximum (4, 8 e^{4})

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

f (x, y) = x^{3} + y^{3} - 3 x^{2} - 3 y^{2} - 9 x

x^{2} - 2 x

g (x, y) = 2 x^{2} + 3 y^{2} - 7

f (x, y) = x^{3} + 2 x y + y^{2} - 5 x

What is the extreme f(x)=e^x(24-x^2) ?
The extreme f(x)=e^x(24-x^2) is Minimum(-6,-(12)/(e^6)),Maximum(4,8e^4)