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Popular Functions >

inflection x^3(x+5)^2+5

Solution

inflection points

x^{3} (x + 5)^{2} + 5

Solution

(- \frac{3 2 + 3}{2}, - \frac{207 2 - 21 3}{4 2} + 5), (\frac{- 6 + 6}{2}, \frac{- 207 2 - 21 3}{4 2} + 5), (0, 5)

Solution steps

f^{''} (x) = 5 (4 x^{3} + 24 x^{2} + 30 x)

Find intervals:

Concave Downward

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

Concave Upward

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

Concave Downward

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

Concave Upward

: 0 < x < \infty

Plug

x = - \frac{3 2 + 3}{2}

into

x^{3} (x + 5)^{2} + 5 : - \frac{207 2 - 21 3}{4 2} + 5

(- \frac{3 2 + 3}{2}, - \frac{207 2 - 21 3}{4 2} + 5)

Plug

x = \frac{- 6 + 6}{2}

into

x^{3} (x + 5)^{2} + 5 : \frac{- 207 2 - 21 3}{4 2} + 5

(\frac{- 6 + 6}{2}, \frac{- 207 2 - 21 3}{4 2} + 5)

Plug

x = 0

into

x^{3} (x + 5)^{2} + 5 : 5

(0, 5)

(- \frac{3 2 + 3}{2}, - \frac{207 2 - 21 3}{4 2} + 5), (\frac{- 6 + 6}{2}, \frac{- 207 2 - 21 3}{4 2} + 5), (0, 5)

Graph

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Frequently Asked Questions (FAQ)

What is the inflection x^3(x+5)^2+5 ?
The inflection x^3(x+5)^2+5 is