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Popular >

extreme x^3-12x+16

Solution

extreme points

x^{3} - 12 x + 16

Solution

Maximum (- 2, 32), Minimum (2, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

x^{3} - 12 x + 16 : 32

Maximum (- 2, 32)

Plug

x = 2

into

x^{3} - 12 x + 16 : 0

Minimum (2, 0)

Maximum (- 2, 32), Minimum (2, 0)

Popular Examples

extreme x^3-12x+12 extreme points

x^{3} - 12 x + 12

extreme f(x,y)=x^2+5xy+y^2-2x+4y+5 extreme points

f (x, y) = x^{2} + 5 x y + y^{2} - 2 x + 4 y + 5

extreme f(x,y)=9xy+(1000)/y+(1000)/x extreme points

f (x, y) = 9 x y + \frac{1000}{y} + \frac{1000}{x}

extreme f(x)=-2x+6x^{2/3},-8<= x<= 4.5 extreme points

f (x) = - 2 x + 6 x^{\frac{2}{3}}, - 8 \leq x \leq 4.5

extreme f(x)=5(x^2+4)^2(x-4)^3 extreme points

f (x) = 5 (x^{2} + 4)^{2} (x - 4)^{3}

Frequently Asked Questions (FAQ)

What is the extreme x^3-12x+16 ?
The extreme x^3-12x+16 is Maximum(-2,32),Minimum(2,0)