What is the inflection f(x)=-x^4-5x^3+7x-3 ?

The inflection f(x)=-x^4-5x^3+7x-3 is (-5/2 , 297/16),(0,-3)

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inflection f(x)=-x^4-5x^3+7x-3

inflection

(- \frac{5}{2}, \frac{297}{16}), (0, - 3)

Solution steps

f^{''} (x) = - 12 x^{2} - 30 x

Find intervals:

Concave Downward

: - \infty < x < - \frac{5}{2},

Concave Upward

: - \frac{5}{2} < x < 0,

Concave Downward

: 0 < x < \infty

Plug

x = - \frac{5}{2}

into

- x^{4} - 5 x^{3} + 7 x - 3 : \frac{297}{16}

(- \frac{5}{2}, \frac{297}{16})

Plug

x = 0

into

- x^{4} - 5 x^{3} + 7 x - 3 : - 3

(0, - 3)

(- \frac{5}{2}, \frac{297}{16}), (0, - 3)

What is the inflection f(x)=-x^4-5x^3+7x-3 ?
The inflection f(x)=-x^4-5x^3+7x-3 is (-5/2 , 297/16),(0,-3)