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Popular >

extreme e^x(24-x^2)

Solution

extreme points

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

Solution

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})

Popular Examples

extreme x^3+3xy^2-15x-12y extreme points

x^{3} + 3 x y^{2} - 15 x - 12 y

extreme f(x)=x+4/(x+1)extreme points

f (x) = x + \frac{4}{x + 1}

extreme f(t,1)=4-x^2-4y^2 extreme points

f (t, 1) = 4 - x^{2} - 4 y^{2}

extreme f(x)=2x^3-15x^2+24x extreme points

f (x) = 2 x^{3} - 15 x^{2} + 24 x

extreme f(x,y)=y^4+x^2-8y^2+2x extreme points

f (x, y) = y^{4} + x^{2} - 8 y^{2} + 2 x

Frequently Asked Questions (FAQ)

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