What is the inflection f(x)=-x^4-7x^3+3x+8 ?

The inflection f(x)=-x^4-7x^3+3x+8 is (-7/2 , 2361/16),(0,8)

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inflection f(x)=-x^4-7x^3+3x+8

inflection points

f (x) = - x^{4} - 7 x^{3} + 3 x + 8

(- \frac{7}{2}, \frac{2361}{16}), (0, 8)

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} + 3 x + 8 : \frac{2361}{16}

(- \frac{7}{2}, \frac{2361}{16})

Plug

x = 0

into

- x^{4} - 7 x^{3} + 3 x + 8 : 8

(0, 8)

(- \frac{7}{2}, \frac{2361}{16}), (0, 8)

5 - x + 1

\frac{x ^{3}}{( x - 1 ) ^{2}}

r (x) = \frac{5 x ^{3}}{x ^{3} + 2 x ^{2} + 5 x}

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

f (x) = - x^{2} - 8

What is the inflection f(x)=-x^4-7x^3+3x+8 ?
The inflection f(x)=-x^4-7x^3+3x+8 is (-7/2 , 2361/16),(0,8)