SOLUTION: f(x)=((x^2)+x)^(2/3);[-2,3]..find the local maximum and local minimum

Algebra ->  Coordinate-system -> SOLUTION: f(x)=((x^2)+x)^(2/3);[-2,3]..find the local maximum and local minimum      Log On


   

Question 696129: f(x)=((x^2)+x)^(2/3);[-2,3]..find the local maximum and local minimum
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a local minimum is:
f%28x%29+=+0 for all x in the interval [-2,3]
%28%28x%5E2%29%2Bx%29%5E%282%2F3%29=0
root%283%2C%28x%5E2%2Bx%29%5E2%29=0....it will be equal to zero if
%28x%5E2%2Bx%29%5E2=0....it will be equal to zero if
x%5E2%2Bx=0
x%28x%2B1%29=0....it will be equal to zero if
x=0
or
x%2B1=0....=>..x=-1
both solutions, x=0 and x=-1 lie in given interval: -2%3C0%3C3, and -2%3C-1%3C3
so, a local minimum is at:(0,0) and (0,0)
+graph%28+600%2C600%2C+-5%2C+5%2C+-5%2C+5%2C+%28%28x%5E2%29%2Bx%29%5E%282%2F3%29%29+
as you can see from a graph, there is no local+maximum