What is the inflection f(x)=6x^4+16x^3 ?

The inflection f(x)=6x^4+16x^3 is (-4/3 ,-512/27),(0,0)

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inflection f(x)=6x^4+16x^3

inflection points

f (x) = 6 x^{4} + 16 x^{3}

(- \frac{4}{3}, - \frac{512}{27}), (0, 0)

Solution steps

f^{''} (x) = 72 x^{2} + 96 x

Find intervals:

Concave Upward

: - \infty < x < - \frac{4}{3},

Concave Downward

: - \frac{4}{3} < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - \frac{4}{3}

into

6 x^{4} + 16 x^{3} : - \frac{512}{27}

(- \frac{4}{3}, - \frac{512}{27})

Plug

x = 0

into

6 x^{4} + 16 x^{3} : 0

(0, 0)

(- \frac{4}{3}, - \frac{512}{27}), (0, 0)

3 x + 2 y = 12

0.00225 x^{2} + 5999.9325 x + 0.50625

f (x) = 8 x + 3

x^{\frac{16}{17}} - x^{\frac{33}{17}}

f (x) = ln (x + 2)

What is the inflection f(x)=6x^4+16x^3 ?
The inflection f(x)=6x^4+16x^3 is (-4/3 ,-512/27),(0,0)