What is the inflection f(x)=-x^4-7x^3+2x-6 ?

The inflection f(x)=-x^4-7x^3+2x-6 is (-7/2 , 2193/16),(0,-6)

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inflection f(x)=-x^4-7x^3+2x-6

inflection points

f (x) = - x^{4} - 7 x^{3} + 2 x - 6

(- \frac{7}{2}, \frac{2193}{16}), (0, - 6)

Solution steps

f^{''} (x) = - 12 x^{2} - 42 x

Find intervals:

Concave Downward

: - \infty < x < - \frac{7}{2},

Concave Upward

: - \frac{7}{2} < x < 0,

Concave Downward

: 0 < x < \infty

Plug

x = - \frac{7}{2}

into

- x^{4} - 7 x^{3} + 2 x - 6 : \frac{2193}{16}

(- \frac{7}{2}, \frac{2193}{16})

Plug

x = 0

into

- x^{4} - 7 x^{3} + 2 x - 6 : - 6

(0, - 6)

(- \frac{7}{2}, \frac{2193}{16}), (0, - 6)

(2.8) (6.4)

f (x) = \frac{( 2 x - 7 )}{3 x + 5}

f (x) = \frac{x}{x ^{2} - 16}

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

f (x) = 2 x^{4} - 3 x^{2} + 1

What is the inflection f(x)=-x^4-7x^3+2x-6 ?
The inflection f(x)=-x^4-7x^3+2x-6 is (-7/2 , 2193/16),(0,-6)