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Popular >

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

Solution

inflection points

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

Solution

(- \frac{3}{2}, - \frac{81}{16}), (0, 0)

Solution steps

f^{''} (x) = 12 x^{2} + 18 x

Find intervals:

Concave Upward

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

Concave Downward

: - \frac{3}{2} < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

x^{4} + 3 x^{3} : - \frac{81}{16}

(- \frac{3}{2}, - \frac{81}{16})

Plug

x = 0

into

x^{4} + 3 x^{3} : 0

(0, 0)

(- \frac{3}{2}, - \frac{81}{16}), (0, 0)

Popular Examples

domain of 2x^2-20x-6 domain

2 x^{2} - 20 x - 6

midpoint (3.5,2.2),(1.5,-4.8)midpoint

(3.5, 2.2), (1.5, - 4.8)

asymptotes of f(x)=-2 asymptotes

f (x) = - 2

domain of sqrt(3x-4)domain

3 x - 4

asymptotes of f(x)=(5x)/(sqrt(9x^2+4))asymptotes

f (x) = \frac{5 x}{9 x ^{2} + 4}

Frequently Asked Questions (FAQ)

What is the inflection f(x)=x^4+3x^3 ?
The inflection f(x)=x^4+3x^3 is (-3/2 ,-81/16),(0,0)