What is the inflection f(x)=-9x^4-12x^3 ?

The inflection f(x)=-9x^4-12x^3 is (-2/3 , 16/9),(0,0)

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inflection f(x)=-9x^4-12x^3

inflection points

f (x) = - 9 x^{4} - 12 x^{3}

(- \frac{2}{3}, \frac{16}{9}), (0, 0)

Solution steps

f^{''} (x) = - 108 x^{2} - 72 x

Find intervals:

Concave Downward

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

Concave Upward

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

Concave Downward

: 0 < x < \infty

Plug

x = - \frac{2}{3}

into

- 9 x^{4} - 12 x^{3} : \frac{16}{9}

(- \frac{2}{3}, \frac{16}{9})

Plug

x = 0

into

- 9 x^{4} - 12 x^{3} : 0

(0, 0)

(- \frac{2}{3}, \frac{16}{9}), (0, 0)

f (x) = 4 - 3 x

f (x) = 4 - 3 sin (\frac{2}{5} (x + 1))

f (x) = 4 x - 5

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

(- 2.4) (10.13)

What is the inflection f(x)=-9x^4-12x^3 ?
The inflection f(x)=-9x^4-12x^3 is (-2/3 , 16/9),(0,0)