What is the inflection f(x)= 1/2 x^4+2x^3 ?

The inflection f(x)= 1/2 x^4+2x^3 is (-2,-8),(0,0)

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inflection f(x)= 1/2 x^4+2x^3

inflection points

f (x) = \frac{1}{2} x^{4} + 2 x^{3}

(- 2, - 8), (0, 0)

Solution steps

f^{''} (x) = 6 x^{2} + 12 x

Find intervals:

Concave Upward

: - \infty < x < - 2,

Concave Downward

: - 2 < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - 2

into

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

(- 2, - 8)

Plug

x = 0

into

\frac{1}{2} x^{4} + 2 x^{3} : 0

(0, 0)

(- 2, - 8), (0, 0)

What is the inflection f(x)= 1/2 x^4+2x^3 ?
The inflection f(x)= 1/2 x^4+2x^3 is (-2,-8),(0,0)