posted by Frank .
Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8-x)).And then the second derivative of this to show by the second derivative test that it is a local maximum. This has been difficult to put into form here.Many thanks.
First we calculate
Equate it to zero and solve for x
Square both sides:
Solve the quadratic to get
Verify both roots (because we squared) and reject x=4-2√2
That leaves us with
Verify that f"(x) <0 at x=4+√2 and hence a maximum.