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

The inflection f(x)=3x^4+8x^3 is (-4/3 ,-256/27),(0,0)

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

inflection points

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

(- \frac{4}{3}, - \frac{256}{27}), (0, 0)

Solution steps

f^{''} (x) = 36 x^{2} + 48 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

3 x^{4} + 8 x^{3} : - \frac{256}{27}

(- \frac{4}{3}, - \frac{256}{27})

Plug

x = 0

into

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

(0, 0)

(- \frac{4}{3}, - \frac{256}{27}), (0, 0)

y = 2 x + 1

f (x) = 6 tan (π x)

lo g_{10} (x)

\frac{1}{3 x ^{2} + 3 x - 18}

x + 9

What is the inflection f(x)=3x^4+8x^3 ?
The inflection f(x)=3x^4+8x^3 is (-4/3 ,-256/27),(0,0)