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Popular >

extreme e^x(15-x^2)

Solution

extreme points

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

Solution

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})

Popular Examples

extreme f(x)=-2/5 x^5-5x^4-16x^3-5 extreme points

f (x) = - \frac{2}{5} x^{5} - 5 x^{4} - 16 x^{3} - 5

extreme g(x,y)=sqrt(16-x^2+y^2)extreme points

g (x, y) = 16 - x^{2} + y^{2}

extreme f(x)=e^{-x-y}extreme points

f (x) = e^{- x - y}

extreme f(x)=x^4-x^2 extreme points

f (x) = x^{4} - x^{2}

extreme f(x)=(1+x^2)/x extreme points

f (x) = \frac{1 + x ^{2}}{x}

Frequently Asked Questions (FAQ)

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