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Popular >

extreme y=2+12x-x^3

Solution

extreme points

y = 2 + 12 x - x^{3}

Solution

Minimum (- 2, - 14), Maximum (2, 18)

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

2 + 12 x - x^{3} : - 14

Minimum (- 2, - 14)

Plug

x = 2

into

2 + 12 x - x^{3} : 18

Maximum (2, 18)

Minimum (- 2, - 14), Maximum (2, 18)

Popular Examples

extreme y=(x^3)/3-2x^2-5x extreme points

y = \frac{x ^{3}}{3} - 2 x^{2} - 5 x

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

f (x) = x^{3} - 3 x^{2} + 12, - 2 \leq x \leq 4

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

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

extreme f(x)=6x+12y-x^2-3y^2 extreme points

f (x) = 6 x + 12 y - x^{2} - 3 y^{2}

extreme f(x)=-0.002x^2+4.4x-10 extreme points

f (x) = - 0.002 x^{2} + 4.4 x - 10

Frequently Asked Questions (FAQ)

What is the extreme y=2+12x-x^3 ?
The extreme y=2+12x-x^3 is Minimum(-2,-14),Maximum(2,18)