What is the inflection y=-x^4-5x^3+6x+7 ?

The inflection y=-x^4-5x^3+6x+7 is (-5/2 , 497/16),(0,7)

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inflection y=-x^4-5x^3+6x+7

inflection points

y = - x^{4} - 5 x^{3} + 6 x + 7

(- \frac{5}{2}, \frac{497}{16}), (0, 7)

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 + 7 : \frac{497}{16}

(- \frac{5}{2}, \frac{497}{16})

Plug

x = 0

into

- x^{4} - 5 x^{3} + 6 x + 7 : 7

(0, 7)

(- \frac{5}{2}, \frac{497}{16}), (0, 7)

y = x + 3

f (x) = - x - 6

- \frac{8 x}{x ^{2} + 2}

f (x) = 8 - 10 x

x - 3

What is the inflection y=-x^4-5x^3+6x+7 ?
The inflection y=-x^4-5x^3+6x+7 is (-5/2 , 497/16),(0,7)