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Popular >

extreme-x^3+12x

Solution

extreme points

- x^{3} + 12 x

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

- x^{3} + 12 x : - 16

Minimum (- 2, - 16)

Plug

x = 2

into

- x^{3} + 12 x : 16

Maximum (2, 16)

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

Popular Examples

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

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

extreme y=x^2-12x+1 extreme points

y = x^{2} - 12 x + 1

extreme (-4)/(x^3)+(30)/((10x+3)^2)extreme points

\frac{- 4}{x ^{3}} + \frac{30}{( 10 x + 3 ) ^{2}}

extreme (x-2)^3 extreme points

(x - 2)^{3}

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

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

Frequently Asked Questions (FAQ)

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