# calculus

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
f(x) = x3 + x − 9, [0, 2]

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1. Well, the short answer is yes, because the function is continuous and continuously differentiable.
However you probably want to find a point in the interval where the tangent slope is the same as the slope of the line between end points
so
(0 , -9) to (2, 0)
slope = (0 - -9) / 2 = 4.5
where does dy/dx = 4.5 ?
dy/dx = 3 x^2 + 1
4.5 = 3 x^2 + 1
x^2 = 3.5/ 3
yes, x is between 0 and 2

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Damon

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