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Popular >

extreme x(x-2)^2

Solution

extreme points

x (x - 2)^{2}

Solution

Maximum (\frac{2}{3}, \frac{32}{27}), Minimum (2, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{2}{3},

Decreasing

: \frac{2}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = \frac{2}{3}

into

x (x - 2)^{2} : \frac{32}{27}

Maximum (\frac{2}{3}, \frac{32}{27})

Plug

x = 2

into

x (x - 2)^{2} : 0

Minimum (2, 0)

Maximum (\frac{2}{3}, \frac{32}{27}), Minimum (2, 0)

Popular Examples

extreme f(x)=xsqrt(15-x)extreme points

f (x) = x 15 - x

extreme Z(x,y)=e^{xy}(x-2y)extreme points

Z (x, y) = e^{x y} (x - 2 y)

extreme f(x)=(x^2-8x+37)/(x-6)extreme points

f (x) = \frac{x ^{2} - 8 x + 37}{x - 6}

extreme f(x)=x^4+8x^3+18x^2+2 extreme points

f (x) = x^{4} + 8 x^{3} + 18 x^{2} + 2

extreme 89e^{x^4}+11 extreme points

89 e^{x^{4}} + 11

Frequently Asked Questions (FAQ)

What is the extreme x(x-2)^2 ?
The extreme x(x-2)^2 is Maximum(2/3 , 32/27),Minimum(2,0)