What is the inflection f(x)=6x^4+8x^3 ?

The inflection f(x)=6x^4+8x^3 is (-2/3 ,-32/27),(0,0)

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inflection f(x)=6x^4+8x^3

inflection points

f (x) = 6 x^{4} + 8 x^{3}

(- \frac{2}{3}, - \frac{32}{27}), (0, 0)

Solution steps

f^{''} (x) = 72 x^{2} + 48 x

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

: 0 < x < \infty

Plug

x = - \frac{2}{3}

into

6 x^{4} + 8 x^{3} : - \frac{32}{27}

(- \frac{2}{3}, - \frac{32}{27})

Plug

x = 0

into

6 x^{4} + 8 x^{3} : 0

(0, 0)

(- \frac{2}{3}, - \frac{32}{27}), (0, 0)

y = \frac{2 x ^{3} + 2}{x ^{2}}

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

f (x) = (x^{3} + 8)^{5}

\frac{x ^{3}}{x ^{2} + 1}

f (x) = 5 x - 4

What is the inflection f(x)=6x^4+8x^3 ?
The inflection f(x)=6x^4+8x^3 is (-2/3 ,-32/27),(0,0)