SOLUTION: Determine whether the Mean Value Theorem applies to the function f(x)=7-x^2 on the interval [-1,2]. if so, find the points that are guaranteed to exist by Mean Value Theorem.

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Question 1155520: Determine whether the Mean Value Theorem applies to the function f(x)=7-x^2 on the interval [-1,2]. if so, find the points that are guaranteed to exist by Mean Value Theorem.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The given function is a polynomial; it is everywhere continuous and differentiable, so the MVT applies.

f(-1) = 6; f(2) = 3; the two endpoints of the specified interval are (-1,6) and (2,3).

The slope of the secant determined by those two points is -1.

We need to find the point(s) in the specified interval where the derivative is equal to -1.

df%2Fdx+=+-2x+=+-1
x+=+.5

The point that is guaranteed by the MVT is (.5,6.75).