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

The inflection x^2sqrt(5+x) is ((2(sqrt(6)-6))/3 ,((56-16sqrt(6))sqrt(3+2\sqrt{6)})/(3sqrt(3)))

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inflection x^2sqrt(5+x)

inflection points

x^{2} 5 + x

(\frac{2 ( 6 - 6 )}{3}, \frac{( 56 - 16 6 ) 3 + 2 6}{3 3})

Solution steps

f^{''} (x) = \frac{15 x ^{2} + 120 x + 200}{4 ( 5 + x ) 5 + x}

Find intervals:

Concave Downward

: - 5 < x < \frac{2 ( 6 - 6 )}{3},

Concave Upward

: \frac{2 ( 6 - 6 )}{3} < x < \infty

Plug

x = \frac{2 ( 6 - 6 )}{3}

into

x^{2} 5 + x : \frac{( 56 - 16 6 ) 3 + 2 6}{3 3}

(\frac{2 ( 6 - 6 )}{3}, \frac{( 56 - 16 6 ) 3 + 2 6}{3 3})

- 2 x^{2} + 3 x - 1

(1, 3), (4, - 3)

(- 2, - 8), (4, 4)

\frac{- x}{3}

y - 1 = \frac{3}{5} (x + 5)

What is the inflection x^2sqrt(5+x) ?
The inflection x^2sqrt(5+x) is ((2(sqrt(6)-6))/3 ,((56-16sqrt(6))sqrt(3+2\sqrt{6)})/(3sqrt(3)))