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About the Class
Calculus as a whole is divided into differentiation and integration.
This session would give you an insight on how to find the maximum and minimum values of a function, which is the basis of differentiation. A function f(x) has a relative maximum value at x = a, if f(a) is greater than any value in its immediate neighborhood. We call it a "relative" maximum because other values of the function may in fact be greater. Similarly, we say that a function f(x) has a relative minimum value at x = b, if f(b) is less than any value in its immediate neighborhood. Again, other values of the function may in fact be less. With that understanding, then, we will drop the term relative. The value of the function, the value of y, at either a maximum or a minimum is called an extreme value. An extreme value is characterized by the tangent to the curve being horizontal. The slope of each tangent line -- the derivative when evaluated at a or b -- is 0 i.e. f ''(x) = 0. Moreover, at points immediately to the left of a maximum -- at a point C -- the slope of the tangent is positive: f ''(x) > 0. While at points immediately to the right -- at a point D -- the slope is negative: f ''(x) < 0. In other words, at a maximum, f ''(x) changes sign from + to - . At a minimum, f ''(x) changes sign from - to + . We can see that at the points E and F.
The presenter would also discuss a detailed step by step process of finding the values. Number of examples would be used to describe the same.
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Keywords: calculus, differentiation, integration