What is the extreme x^{1/3}(x+3)^{2/3} ?

The extreme x^{1/3}(x+3)^{2/3} is Maximum(-3,0),Minimum(-1,-2^{2/3})

Popular >

extreme x^{1/3}(x+3)^{2/3}

extreme points

x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}}

Maximum (- 3, 0), Minimum (- 1, - 2^{\frac{2}{3}})

Solution steps

f^{'} (x) = \frac{x + 1}{x ^{\frac{2}{3}} ( x + 3 ) ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}} : 0

Maximum (- 3, 0)

Plug

x = - 1

into

x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}} : - 2^{\frac{2}{3}}

Minimum (- 1, - 2^{\frac{2}{3}})

Maximum (- 3, 0), Minimum (- 1, - 2^{\frac{2}{3}})

f (x) = 6 x^{2} - 24 x + 18

f (x) = x (17 - 45 + 2 x) (\frac{45}{2} - x)

f (x) = x^{4} (x - 3)^{3}

f (x) = - x^{3} + 12 x^{2} + 45 x - 52

f (x) = (x - 1)^{2} + (4 - 4 x^{2})

What is the extreme x^{1/3}(x+3)^{2/3} ?
The extreme x^{1/3}(x+3)^{2/3} is Maximum(-3,0),Minimum(-1,-2^{2/3})