What is the inflection f(x)=6x^4+32x^3 ?

The inflection f(x)=6x^4+32x^3 is (-8/3 ,-8192/27),(0,0)

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inflection f(x)=6x^4+32x^3

inflection points

f (x) = 6 x^{4} + 32 x^{3}

(- \frac{8}{3}, - \frac{8192}{27}), (0, 0)

Solution steps

f^{''} (x) = 72 x^{2} + 192 x

Find intervals:

Concave Upward

: - \infty < x < - \frac{8}{3},

Concave Downward

: - \frac{8}{3} < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - \frac{8}{3}

into

6 x^{4} + 32 x^{3} : - \frac{8192}{27}

(- \frac{8}{3}, - \frac{8192}{27})

Plug

x = 0

into

6 x^{4} + 32 x^{3} : 0

(0, 0)

(- \frac{8}{3}, - \frac{8192}{27}), (0, 0)

f (x) = 5 x^{5}

\frac{x - 1}{x}

(- 4 - 7) (- 4 - 6)

f (x) = x - 1

f (x) = 5 x^{2} - 2 x - 3

What is the inflection f(x)=6x^4+32x^3 ?
The inflection f(x)=6x^4+32x^3 is (-8/3 ,-8192/27),(0,0)