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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).
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Alternate Notation : Next we have to discuss some alternate notation for the derivative. The typical derivative notation is the "prime" notation. Though, there is another notation
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NULL/ VOID/ EMPTY SET A set which has no element is known as the null set or empty set and is indicated by f (phi). The number of elements of a set A is indicated as n (A) and
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