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Popular >

inflection f(x)=x(x-4)^3

Solution

inflection points

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

Solution

(2, - 16), (4, 0)

Solution steps

f^{''} (x) = 4 (3 x^{2} - 18 x + 24)

Find intervals:

Concave Upward

: - \infty < x < 2,

Concave Downward

: 2 < x < 4,

Concave Upward

: 4 < x < \infty

Plug

x = 2

into

x (x - 4)^{3} : - 16

(2, - 16)

Plug

x = 4

into

x (x - 4)^{3} : 0

(4, 0)

(2, - 16), (4, 0)

Popular Examples

inflection (x^2)/(x-1)inflection points

\frac{x ^{2}}{x - 1}

domain of f(x)= 1/(2sqrt(x))domain

f (x) = \frac{1}{2 x}

asymptotes of (4x+1)/(16x^2+1)asymptotes

\frac{4 x + 1}{16 x ^{2} + 1}

critical x^{10/11}-x^{21/11}critical points

x^{\frac{10}{11}} - x^{\frac{21}{11}}

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

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

Frequently Asked Questions (FAQ)

What is the inflection f(x)=x(x-4)^3 ?
The inflection f(x)=x(x-4)^3 is (2,-16),(4,0)