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Popular >

inflection f(x)=x^4-2x^3

Solution

inflection points

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

Solution

(0, 0), (1, - 1)

Solution steps

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

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < 1,

Concave Upward

: 1 < x < \infty

Plug

x = 0

into

x^{4} - 2 x^{3} : 0

(0, 0)

Plug

x = 1

into

x^{4} - 2 x^{3} : - 1

(1, - 1)

(0, 0), (1, - 1)

Popular Examples

extreme x+sqrt(1-x)extreme points

x + 1 - x

critical 2x^3-2x^2+7x+5 critical points

2 x^{3} - 2 x^{2} + 7 x + 5

range of y=9sqrt(x)+4 range

y = 9 x + 4

line (0,0),(4,5)line

(0, 0), (4, 5)

asymptotes of (8x^2+1)/(4x^3-2x^2+1)asymptotes

\frac{8 x ^{2} + 1}{4 x ^{3} - 2 x ^{2} + 1}

Frequently Asked Questions (FAQ)

What is the inflection f(x)=x^4-2x^3 ?
The inflection f(x)=x^4-2x^3 is (0,0),(1,-1)