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Popular >

extreme (e^x)/(x^4)

Solution

extreme points

\frac{e ^{x}}{x ^{4}}

Solution

Minimum (4, \frac{e ^{4}}{256})

Solution steps

f^{'} (x) = \frac{e ^{x} ( x - 4 )}{x ^{5}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 4

into

\frac{e ^{x}}{x ^{4}} : \frac{e ^{4}}{256}

Minimum (4, \frac{e ^{4}}{256})

Popular Examples

extreme F(x,y)=x^2+xy+y^2+3x-3y+4 extreme points

F (x, y) = x^{2} + x y + y^{2} + 3 x - 3 y + 4

extreme f(x,y)=6-2x+4y-x^2-4y^2 extreme points

f (x, y) = 6 - 2 x + 4 y - x^{2} - 4 y^{2}

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

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

extreme f(x)=5x^2-10x+2,-4<= x<= 2 extreme points

f (x) = 5 x^{2} - 10 x + 2, - 4 \leq x \leq 2

extreme f(x)=x+sin(x),-pi/2 <= x<= pi/2 extreme points

f (x) = x + sin (x), - \frac{π}{2} \leq x \leq \frac{π}{2}

Frequently Asked Questions (FAQ)

What is the extreme (e^x)/(x^4) ?
The extreme (e^x)/(x^4) is Minimum(4,(e^4)/(256))