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Calculus/AP Calculus BC

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Expert: - 11/16/2008


Question
Determine whether Means Value Theorem can be applied to f on the closed interval [a,b], if so, find all values of c in the open interval [a,b]
a) f(x)=x(x^2-x-2), [-1,1]

Answer
The function should be multiplied our to give
f(x) = x^3 - x² - 2x.

Each of these (x^3, -x², and -2x) is continuous on [-1,1], so when they are added together, they are still continuous.

Integrate the f(x) from -1 ot 1 and get I.  Note that the width of the integral is 2, so set f(x) = I/2 and solve.

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