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Popular >

extreme 12+6x^2-x^3

Solution

extreme points

12 + 6 x^{2} - x^{3}

Solution

Minimum (0, 12), Maximum (4, 44)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

12 + 6 x^{2} - x^{3} : 12

Minimum (0, 12)

Plug

x = 4

into

12 + 6 x^{2} - x^{3} : 44

Maximum (4, 44)

Minimum (0, 12), Maximum (4, 44)

Popular Examples

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f (x, y) = x^{4} + x^{2} - 6 x y + 3 y^{2}

extreme f(x,y)=3x+3y extreme points

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

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

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

extreme f(x)= 1/4 x^4-4/3 x^3+2x^2 extreme points

f (x) = \frac{1}{4} x^{4} - \frac{4}{3} x^{3} + 2 x^{2}

Frequently Asked Questions (FAQ)

What is the extreme 12+6x^2-x^3 ?
The extreme 12+6x^2-x^3 is Minimum(0,12),Maximum(4,44)