Let f(x) = \sin(x)+\cos^2(x). Find all points of absolute minima and maxima on the interval [0,\pi]. As your answer, input the sum of the values of f at all points the absolute minima and maxima occur in the given interval.

To find the points of absolute minima and maxima of the function \( f(x) = \sin(x) + \cos^2(x) \) on the interval \([0, \pi]\), we will follow these steps:

1. Find the derivative of \( f(x) \).
2. Determine the critical points by setting the derivative equal to zero.
3. Evaluate \( f(x) \) at the critical points and at the endpoints of the interval \([0, \pi]\).
4. Identify the absolute

Let f(x) = \sin(x) + \cos^2(x). Find all points of absolute minima and maxima on the interval [0,\pi]. As your answer, input the sum of the values of f at all points the absolute minima and maxima occur in the given interval.

This problem involves determining the absolute minima and maxima of the function f(x) = sin(x) + cos^2(x) over the interval [0, π]. Learn how to apply calculus principles, including critical points and the first derivative test, to find the extrema values.

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