What is the inflection 6x^4+2x^3-12x^2+3 ?

The inflection 6x^4+2x^3-12x^2+3 is (-2/3 ,-47/27),(1/2 , 5/8)

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inflection 6x^4+2x^3-12x^2+3

inflection points

6 x^{4} + 2 x^{3} - 12 x^{2} + 3

(- \frac{2}{3}, - \frac{47}{27}), (\frac{1}{2}, \frac{5}{8})

Solution steps

f^{''} (x) = 72 x^{2} + 12 x - 24

Find intervals:

Concave Upward

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

Concave Downward

: - \frac{2}{3} < x < \frac{1}{2},

Concave Upward

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

Plug

x = - \frac{2}{3}

into

6 x^{4} + 2 x^{3} - 12 x^{2} + 3 : - \frac{47}{27}

(- \frac{2}{3}, - \frac{47}{27})

Plug

x = \frac{1}{2}

into

6 x^{4} + 2 x^{3} - 12 x^{2} + 3 : \frac{5}{8}

(\frac{1}{2}, \frac{5}{8})

(- \frac{2}{3}, - \frac{47}{27}), (\frac{1}{2}, \frac{5}{8})

(x + 3)^{2}

f (x) = \frac{8 x ^{2} + 1}{2 x ^{2} + 3 x - 2}

f (x) = \frac{1 - x}{x}

5 + x + 5

f (x) = 5 x - 9

What is the inflection 6x^4+2x^3-12x^2+3 ?
The inflection 6x^4+2x^3-12x^2+3 is (-2/3 ,-47/27),(1/2 , 5/8)