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

The inflection f(x)=-x^4-5x^3+5x+3 is (-5/2 , 473/16),(0,3)

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

inflection points

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

(- \frac{5}{2}, \frac{473}{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} + 5 x + 3 : \frac{473}{16}

(- \frac{5}{2}, \frac{473}{16})

Plug

x = 0

into

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

(0, 3)

(- \frac{5}{2}, \frac{473}{16}), (0, 3)

12 x - 3 y - 6 = 0

f (x) = 3^{x} + 2

5 x - y = 4, (2, 3)

f (x) = 20 - 4 x

f (x) = \frac{x + 6}{2}

What is the inflection f(x)=-x^4-5x^3+5x+3 ?
The inflection f(x)=-x^4-5x^3+5x+3 is (-5/2 , 473/16),(0,3)