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How to find maximum and minimum of (x sinx) in the interval -pi/2 to 3pi/2

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Final answer:

To find the maximum and minimum of (x sinx) in the interval -pi/2 to 3pi/2, we need to find the critical points of the function where the derivative equals zero or does not exist.

Step-by-step explanation:

To find the maximum and minimum of the function (x sinx) in the interval -pi/2 to 3pi/2, we need to find the critical points of the function where the derivative equals zero or does not exist.

First, we find the derivative of the function: f'(x) = sinx + xcosx.

Next, we set f'(x) = 0 and solve for x. The critical points are the values of x where f'(x) = 0 or does not exist.

Finally, we evaluate the function at the critical points and the endpoints of the interval to find the maximum and minimum values.

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