SOLUTION: Determine the maximum function value for the function f(x)=2x/(x+2) on the interval [-1,2]. Thanks :)

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Question 1026259: Determine the maximum function value for the function f(x)=2x/(x+2) on the interval [-1,2].
Thanks :)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+%282x%29%2F%28x%2B2%29 ==> y'=4%2F%28x%2B2%29%5E2.
This function is not differentiable at -2, which is safely outside [-1,2], but will always have a positive derivative whenever it exists. The function is increasing over (-infinity,-2) and (-2,infinity). Thus the maximum value of the function over [-1,2] exists at the endpoint x = 2, with function value f%282%29+=+%282%2A2%29%2F%282%2B2%29+=+1.