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Popular >

extreme (x+1)(x-4)^2

Solution

extreme points

(x + 1) (x - 4)^{2}

Solution

Maximum (\frac{2}{3}, \frac{500}{27}), Minimum (4, 0)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

: \frac{2}{3} < x < 4,

Increasing

: 4 < x < \infty

Plug

x = \frac{2}{3}

into

(x + 1) (x - 4)^{2} : \frac{500}{27}

Maximum (\frac{2}{3}, \frac{500}{27})

Plug

x = 4

into

(x + 1) (x - 4)^{2} : 0

Minimum (4, 0)

Maximum (\frac{2}{3}, \frac{500}{27}), Minimum (4, 0)

Popular Examples

domain of f(x)=(6x+8)/(x^2+4x)domain

f (x) = \frac{6 x + 8}{x ^{2} + 4 x}

domain of f(x)=(14)/(x^2-9x-36)domain

f (x) = \frac{14}{x ^{2} - 9 x - 36}

range of f(x)=2y-3x=-8 range

f (x) = 2 y - 3 x = - 8

extreme f(x)=x^3-12x^2-27x+3 extreme points

f (x) = x^{3} - 12 x^{2} - 27 x + 3

inverse of y=-3(x-1)inverse

y = - 3 (x - 1)

Frequently Asked Questions (FAQ)

What is the extreme (x+1)(x-4)^2 ?
The extreme (x+1)(x-4)^2 is Maximum(2/3 , 500/27),Minimum(4,0)