What is the inflection f(x)=2x^3+3x^2-36x ?

The inflection f(x)=2x^3+3x^2-36x is (-1/2 , 37/2)

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inflection f(x)=2x^3+3x^2-36x

inflection points

f (x) = 2 x^{3} + 3 x^{2} - 36 x

(- \frac{1}{2}, \frac{37}{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} - 36 x : \frac{37}{2}

(- \frac{1}{2}, \frac{37}{2})

f (x) = x + y = - 1

f (x) = \frac{x}{1 + x ^{2}}

x^{4} + 32 x^{2} + 256

f (x) = x x + 1

1 - (x - 3)^{2}

What is the inflection f(x)=2x^3+3x^2-36x ?
The inflection f(x)=2x^3+3x^2-36x is (-1/2 , 37/2)