What is the inflection f(x)=-x^4-3x^3+6x+1 ?

The inflection f(x)=-x^4-3x^3+6x+1 is (-3/2 ,-47/16),(0,1)

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inflection f(x)=-x^4-3x^3+6x+1

inflection points

f (x) = - x^{4} - 3 x^{3} + 6 x + 1

(- \frac{3}{2}, - \frac{47}{16}), (0, 1)

Solution steps

f^{''} (x) = - 12 x^{2} - 18 x

Find intervals:

Concave Downward

: - \infty < x < - \frac{3}{2},

Concave Upward

: - \frac{3}{2} < x < 0,

Concave Downward

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

- x^{4} - 3 x^{3} + 6 x + 1 : - \frac{47}{16}

(- \frac{3}{2}, - \frac{47}{16})

Plug

x = 0

into

- x^{4} - 3 x^{3} + 6 x + 1 : 1

(0, 1)

(- \frac{3}{2}, - \frac{47}{16}), (0, 1)

f (x) = 3 x^{4} - 8 x^{3} + 6 x^{2} + 2

\frac{x ^{2} - 7}{x ^{3} - x ^{2} - 12 x}

y = x^{2} + 4 x + 3

f (x) = \frac{x}{x ^{2} + 1}

f (x) = \frac{5 + x}{2 - x}

What is the inflection f(x)=-x^4-3x^3+6x+1 ?
The inflection f(x)=-x^4-3x^3+6x+1 is (-3/2 ,-47/16),(0,1)