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Rolle's Theorem
Assume f(x) is a function which satisfies all of the following.
1. f(x) is continuous in the closed interval [a,b].
2. f(x) is differentiable in the open interval (a,b).
3. f(a) = f(b)
So, there is a number c as a < c < b and f′(c) = 0. Or, though f(x) has a critical point in (a,b).
Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several
Question: Find Fourier series for the periodic function of period 2 π,defined by f(x) = x 4 , - π ≤ x ≤ π
20+20
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