What is the inflection f(x)=-x^4-5x^3+6x-2 ?

The inflection f(x)=-x^4-5x^3+6x-2 is (-5/2 , 353/16),(0,-2)

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inflection f(x)=-x^4-5x^3+6x-2

inflection points

f (x) = - x^{4} - 5 x^{3} + 6 x - 2

(- \frac{5}{2}, \frac{353}{16}), (0, - 2)

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} + 6 x - 2 : \frac{353}{16}

(- \frac{5}{2}, \frac{353}{16})

Plug

x = 0

into

- x^{4} - 5 x^{3} + 6 x - 2 : - 2

(0, - 2)

(- \frac{5}{2}, \frac{353}{16}), (0, - 2)

What is the inflection f(x)=-x^4-5x^3+6x-2 ?
The inflection f(x)=-x^4-5x^3+6x-2 is (-5/2 , 353/16),(0,-2)