SOLUTION: 3. The function f(x)= (x^2+2x)^2/3: (USE CALCULUS to answer a-e) > > a. Increasing on what interval(s)

SOLUTION: 3. The function f(x)= (x^2+2x)^2/3: (USE CALCULUS to answer a-e) > > a. Increasing on what interval(s) > b. Decreasing on what interval(s) >

Question 55678: 3. The function f(x)= (x^2+2x)^2/3: (USE CALCULUS to answer a-e)
>
> a. Increasing on what interval(s)
> b. Decreasing on what interval(s)
> c. Has critical numbers?
> d. Has Relative Maximum?
> e. Has Relative Minimum?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
3. The function f(x)= (x^2+2x)^2/3: (USE CALCULUS to answer a-e)
f'(x)= (4/3)(x+1)(x^2+2x)^(-1/3)
> a. Increasing on what interval(s)
Increasing when f'(x)>0
f'(x)=0 when x=-1 and f'(x)has a discontinutity at x=-2 and at x=0.
Need to check the intervals (-inf,-2),(-2,-1),(-1,0),(0,+inf)
1st interval: if x=-10 f'(-10)= neg/pos <0; f decreasing on (-inf,-2)
2nd iinterval: if x=(-3/2); f(-3/2)=neg/neg>0; f increasing on (-2,-1)
3rd interval: if x=-1/2 f'(-1/2)=pos/neg<0; f decreasing on (-1,0)
4th interval: if x=10 f'(10)=pos/pos: f inceasing on (0,inf)
----------------
> b. Decreasing on what interval(s)
See "a"
> c. Has critical numbers?
x=-2, x=-1, x=0
> d. Has Relative Maximum?
x=-1
> e. Has Relative Minimum?
At x=-2, x=0
Cheers,
Stan H.

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