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Popular >

extreme f(x)=27x-x^3

Solution

extreme points

f (x) = 27 x - x^{3}

Solution

Minimum (- 3, - 54), Maximum (3, 54)

Solution steps

f^{'} (x) = 27 - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

27 x - x^{3} : - 54

Minimum (- 3, - 54)

Plug

x = 3

into

27 x - x^{3} : 54

Maximum (3, 54)

Minimum (- 3, - 54), Maximum (3, 54)

Popular Examples

extreme f(x,y)=3x^2y+y^3-3x^2-3y^2+2 extreme points

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

extreme f(x)= 1/x+ln(x),e^{-1}<= x<= e extreme points

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

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

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extreme f(x)=3x^4-4x^3-12x^2+17 extreme points

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 17

Frequently Asked Questions (FAQ)

What is the extreme f(x)=27x-x^3 ?
The extreme f(x)=27x-x^3 is Minimum(-3,-54),Maximum(3,54)