What is the inflection f(x)=2x^3+3x^2-12x ?

The inflection f(x)=2x^3+3x^2-12x is (-1/2 , 13/2)

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inflection f(x)=2x^3+3x^2-12x

inflection points

f (x) = 2 x^{3} + 3 x^{2} - 12 x

(- \frac{1}{2}, \frac{13}{2})

Solution steps

f^{''} (x) = 12 x + 6

Find intervals:

Concave Downward

: - \infty < x < - \frac{1}{2},

Concave Upward

: - \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

2 x^{3} + 3 x^{2} - 12 x : \frac{13}{2}

(- \frac{1}{2}, \frac{13}{2})

f (x) = \frac{x ^{3}}{x ^{4} - x ^{2}}

(0, 4), (2, 3)

y = 3 x - 6

x^{3} + x^{2} - 9 x - 9

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

What is the inflection f(x)=2x^3+3x^2-12x ?
The inflection f(x)=2x^3+3x^2-12x is (-1/2 , 13/2)