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Popular >

extreme 4x^3-12x^2

Solution

extreme points

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

Solution

Maximum (0, 0), Minimum (2, - 16)

Solution steps

f^{'} (x) = 12 x^{2} - 24 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 2

into

4 x^{3} - 12 x^{2} : - 16

Minimum (2, - 16)

Maximum (0, 0), Minimum (2, - 16)

Popular Examples

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3 x y - x^{2} y - x y^{2}

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

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

extreme f(x,y)= 1/3 x^3+1/3 y^3-x-y+10 extreme points

f (x, y) = \frac{1}{3} x^{3} + \frac{1}{3} y^{3} - x - y + 10

extreme f(x)=(x^4)/4-8x extreme points

f (x) = \frac{x ^{4}}{4} - 8 x

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

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

Frequently Asked Questions (FAQ)

What is the extreme 4x^3-12x^2 ?
The extreme 4x^3-12x^2 is Maximum(0,0),Minimum(2,-16)