Question 1155520
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The given function is a polynomial; it is everywhere continuous and differentiable, so the MVT applies.<br>
f(-1) = 6; f(2) = 3; the two endpoints of the specified interval are (-1,6) and (2,3).<br>
The slope of the secant determined by those two points is -1.<br>
We need to find the point(s) in the specified interval where the derivative is equal to -1.<br>
{{{df/dx = -2x = -1}}}
{{{x = .5}}}<br>
The point that is guaranteed by the MVT is (.5,6.75).<br>