What is the extreme f(x)=x^{1/3}(x+6)^{2/3} ?

The extreme f(x)=x^{1/3}(x+6)^{2/3} is Maximum(-6,0),Minimum(-2,-2*2^{2/3})

Popular >

extreme f(x)=x^{1/3}(x+6)^{2/3}

extreme points

f (x) = x^{\frac{1}{3}} (x + 6)^{\frac{2}{3}}

Maximum (- 6, 0), Minimum (- 2, - 2 \cdot 2^{\frac{2}{3}})

Solution steps

f^{'} (x) = \frac{x + 2}{x ^{\frac{2}{3}} ( x + 6 ) ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < - 2,

Increasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

x^{\frac{1}{3}} (x + 6)^{\frac{2}{3}} : 0

Maximum (- 6, 0)

Plug

x = - 2

into

x^{\frac{1}{3}} (x + 6)^{\frac{2}{3}} : - 2 \cdot 2^{\frac{2}{3}}

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

Maximum (- 6, 0), Minimum (- 2, - 2 \cdot 2^{\frac{2}{3}})

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 46

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

y = x^{3} + 4 x^{2} + 5 x - 2

\frac{x - 4}{x ^{2}}

y = 4 sin (2 π (x + (- 45))) + (- 2)

What is the extreme f(x)=x^{1/3}(x+6)^{2/3} ?
The extreme f(x)=x^{1/3}(x+6)^{2/3} is Maximum(-6,0),Minimum(-2,-2*2^{2/3})