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Popular >

extreme x(x-4)^2

Solution

extreme points

x (x - 4)^{2}

Solution

Maximum (\frac{4}{3}, \frac{256}{27}), Minimum (4, 0)

Solution steps

f^{'} (x) = (x - 4) (3 x - 4)

Find intervals:

Increasing

: - \infty < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < 4,

Increasing

: 4 < x < \infty

Plug

x = \frac{4}{3}

into

x (x - 4)^{2} : \frac{256}{27}

Maximum (\frac{4}{3}, \frac{256}{27})

Plug

x = 4

into

x (x - 4)^{2} : 0

Minimum (4, 0)

Maximum (\frac{4}{3}, \frac{256}{27}), Minimum (4, 0)

Popular Examples

intercepts of f(x)=(4x^2)/(x^2-9)intercepts

f (x) = \frac{4 x ^{2}}{x ^{2} - 9}

slope of 3+4x=2y-9 slope

3 + 4 x = 2 y - 9

slope ofintercept 3x+2y=-8 slope intercept

3 x + 2 y = - 8

asymptotes of 3(x^2-16)/(x^2-9)asymptotes

3 \frac{x ^{2} - 16}{x ^{2} - 9}

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

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

Frequently Asked Questions (FAQ)

What is the extreme x(x-4)^2 ?
The extreme x(x-4)^2 is Maximum(4/3 , 256/27),Minimum(4,0)