What is the inflection \sqrt[3]{x}(x+4) ?

The inflection \sqrt[3]{x}(x+4) is (0,0),(2,6\sqrt[3]{2})

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inflection \sqrt[3]{x}(x+4)

inflection points

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = 2, x = 0

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

All inflection points are in domain and not on domain edges

x = 0, x = 2

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < 2,

Concave Upward

: 2 < x < \infty

Plug

x = 0

into

(0, 0)

Plug

x = 2

into

y = 5 x

f (x) = 3 x - 5

\frac{y ^{2} - 1}{y}

(1, 4), (4, 8)

f (x) = - \frac{3}{4} x + \frac{15}{4}

What is the inflection \sqrt[3]{x}(x+4) ?
The inflection \sqrt[3]{x}(x+4) is (0,0),(2,6\sqrt[3]{2})