Use calculus to find the absolute maximum and minimum values of the function. (round all answers to three decimal places.) f(x) = x + 2cos(x) [0, 2]olute minimum values of f on the given interval. f(x) = e-x - e-2x [0, 1]

Part A:

Given the function , the absolute maximum or minimum occurs when .



Using the second derivative test,



Since the second derivative gives a negative number, the given function has a maximum point at .

And the maximum point is given by:



i.e.

Part B:

Given the function , the absolute maximum or minimum occurs when .



Using the second derivative test,



Since the second derivative gives a negative number, the given function has a maximum point at .

And the maximum point is given by:



i.e. (0.693, 0.25)

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The volume is 2212m cubed