What is the inflection-3/2 x^4+6x^3+72x^2 ?

The inflection-3/2 x^4+6x^3+72x^2 is (-2,216),(4,1152)

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inflection-3/2 x^4+6x^3+72x^2

inflection points

- \frac{3}{2} x^{4} + 6 x^{3} + 72 x^{2}

(- 2, 216), (4, 1152)

Solution steps

f^{''} (x) = - 18 x^{2} + 36 x + 144

Find intervals:

Concave Downward

: - \infty < x < - 2,

Concave Upward

: - 2 < x < 4,

Concave Downward

: 4 < x < \infty

Plug

x = - 2

into

- \frac{3}{2} x^{4} + 6 x^{3} + 72 x^{2} : 216

(- 2, 216)

Plug

x = 4

into

- \frac{3}{2} x^{4} + 6 x^{3} + 72 x^{2} : 1152

(4, 1152)

(- 2, 216), (4, 1152)

4 x + 10

f (x) = - x^{2} - 2

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

3 x - y + 9 = 0

y = - 3 x + 5

What is the inflection-3/2 x^4+6x^3+72x^2 ?
The inflection-3/2 x^4+6x^3+72x^2 is (-2,216),(4,1152)