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Popular >

extreme y=4x^3-12x

Solution

extreme points

y = 4 x^{3} - 12 x

Solution

Maximum (- 1, 8), Minimum (1, - 8)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

4 x^{3} - 12 x : 8

Maximum (- 1, 8)

Plug

x = 1

into

4 x^{3} - 12 x : - 8

Minimum (1, - 8)

Maximum (- 1, 8), Minimum (1, - 8)

Popular Examples

extreme f(x)=(x-1)(x^2-2x-2)extreme points

f (x) = (x - 1) (x^{2} - 2 x - 2)

extreme f(x,y)=sqrt(400-9x^2-25y^2)extreme points

f (x, y) = 400 - 9 x^{2} - 25 y^{2}

extreme f(x)=(e^x)/(x^5),x>0 extreme points

f (x) = \frac{e ^{x}}{x ^{5}}, x > 0

extreme f(x)=8+3x^2-x^3 extreme points

f (x) = 8 + 3 x^{2} - x^{3}

extreme f(x)=4x^2-16x+4,0<= x<= 3 extreme points

f (x) = 4 x^{2} - 16 x + 4, 0 \leq x \leq 3

Frequently Asked Questions (FAQ)

What is the extreme y=4x^3-12x ?
The extreme y=4x^3-12x is Maximum(-1,8),Minimum(1,-8)