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Popular >

inflection f(x)=x^4-4x^3+1

Solution

inflection points

f (x) = x^{4} - 4 x^{3} + 1

Solution

(0, 1), (2, - 15)

Solution steps

f^{''} (x) = 12 x^{2} - 24 x

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < 2,

Concave Upward

: 2 < x < \infty

Plug

x = 0

into

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

(0, 1)

Plug

x = 2

into

x^{4} - 4 x^{3} + 1 : - 15

(2, - 15)

(0, 1), (2, - 15)

Popular Examples

domain of f(x)= 4/((x+1)^2-1)domain

f (x) = \frac{4}{( x + 1 ) ^{2} - 1}

critical f(x)=x^3-3x critical points

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

domain of f(x)=(x-1)/(x^2+1)domain

f (x) = \frac{x - 1}{x ^{2} + 1}

asymptotes of f(x)=(x^2-5x+6)/(4x+4)asymptotes

f (x) = \frac{x ^{2} - 5 x + 6}{4 x + 4}

range of f(x)=sqrt(1-2x)range

f (x) = 1 - 2 x

Frequently Asked Questions (FAQ)

What is the inflection f(x)=x^4-4x^3+1 ?
The inflection f(x)=x^4-4x^3+1 is (0,1),(2,-15)