SOLUTION: Consider the function f(x) = (x^(4/5))(x-10). Find the the two numbers where f"(x) = 0 or f"(x) is undefined. Also, find the intervals where f(x) is concave up or down.

Question 1201081: Consider the function f(x) = (x^(4/5))(x-10). Find the the two numbers where f"(x) = 0 or f"(x) is undefined. Also, find the intervals where f(x) is concave up or down.
Answer by amarjeeth123(569) (Show Source): You can put this solution on YOUR website!
The given function is f(x)=(x^(4/5))(x-10).
f'(x)=(9x-40)/(5*(x^(1/5)))
f''(x)=(36x+40)/(25*(x^(6/5)))
The points where f"(x)=0 are given by 36x+40=0 or 36x=-40 or x=-(10/9) and x=0.
The points where f"(x)=0 or undefined are x=-(10/9) and x=0.
Concave Downward:(-inf,-10/9)
Concave Upward:(-10/9,0)U(0,inf)

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