What is the inflection x^4+x^3-3x^2+1 ?

The inflection x^4+x^3-3x^2+1 is (-1,-2),(1/2 , 7/16)

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inflection x^4+x^3-3x^2+1

inflection points

x^{4} + x^{3} - 3 x^{2} + 1

(- 1, - 2), (\frac{1}{2}, \frac{7}{16})

Solution steps

f^{''} (x) = 12 x^{2} + 6 x - 6

Find intervals:

Concave Upward

: - \infty < x < - 1,

Concave Downward

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

Concave Upward

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

Plug

x = - 1

into

x^{4} + x^{3} - 3 x^{2} + 1 : - 2

(- 1, - 2)

Plug

x = \frac{1}{2}

into

x^{4} + x^{3} - 3 x^{2} + 1 : \frac{7}{16}

(\frac{1}{2}, \frac{7}{16})

(- 1, - 2), (\frac{1}{2}, \frac{7}{16})

f (x) = x^{4} - 4 x^{3}

f (x) = (x + 4)^{3}

(3, - 6), (5, 8)

sec (x)

\frac{x ^{2}}{x ^{2} - 16}

What is the inflection x^4+x^3-3x^2+1 ?
The inflection x^4+x^3-3x^2+1 is (-1,-2),(1/2 , 7/16)