What is the inflection f(x)=2x^3+3x^2-72x ?

The inflection f(x)=2x^3+3x^2-72x is (-1/2 , 73/2)

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inflection f(x)=2x^3+3x^2-72x

inflection points

f (x) = 2 x^{3} + 3 x^{2} - 72 x

(- \frac{1}{2}, \frac{73}{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} - 72 x : \frac{73}{2}

(- \frac{1}{2}, \frac{73}{2})

m o n o t o n e f (x) = x 64 - x^{2}

in v erse f (- 3) = e^{x - 3}

in v erse f (x) = ln (3 t)

in t erce pt s y = - 1.5 x + 3

f (x) = 3 x + 1

What is the inflection f(x)=2x^3+3x^2-72x ?
The inflection f(x)=2x^3+3x^2-72x is (-1/2 , 73/2)