Determine if the Mean Value Theorem for Integrals applies to the function f(x) = 3 - x2 on the interval the closed interval from 0 to the square root of 3 . If so, find the x-coordinates of the point(s) guaranteed by the theorem

Yes, Mean Value Theorem for Integrals applies for the function and values of x are 1 and -1

Step-by-step explanation: Mean Value Theorem for Integrals states that if a function is continuous on a closed interval, there is a value c on the interval such that

where a and b are the closed interval given

As the graph of shown below, the function is continuous on the interval [0,], so the theorem applies.

To find the x-coordinates, first determine value of f(c) at [0,]:

f(c) = 2

The x-coordinates will be:

x = ±1

The values for x guaranteed by the Mean Value Theorem are +1 and -1.

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