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Popular >

extreme 12x^2-x^3

Solution

extreme points

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

Solution

Minimum (0, 0), Maximum (8, 256)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 8,

Decreasing

: 8 < x < \infty

Plug

x = 0

into

12 x^{2} - x^{3} : 0

Minimum (0, 0)

Plug

x = 8

into

12 x^{2} - x^{3} : 256

Maximum (8, 256)

Minimum (0, 0), Maximum (8, 256)

Popular Examples

range of y=sqrt(x)-5 range

y = x - 5

inverse of (x+7)^3 inverse

(x + 7)^{3}

domain of f(x)=2x^5+3x+1 domain

f (x) = 2 x^{5} + 3 x + 1

inverse of f(x)= 1/3 x+3 inverse

f (x) = \frac{1}{3} x + 3

line m=-12,(2,-8)line

m = - 12, (2, - 8)

Frequently Asked Questions (FAQ)

What is the extreme 12x^2-x^3 ?
The extreme 12x^2-x^3 is Minimum(0,0),Maximum(8,256)