important calculus theorems

Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in measurement,..

If x is a rational number, then the sum (e x ) of the exponential series..

Degree and order of a differential equation How to form a differential equation Types of differential equations and their general solution..

Let f be a differentiable function on I and let x 0 be any interior point of I. Then (a) If f attains its absolute maximum value at x 0 , then f ' (x 0 )= 0 (b) If f attains its absolute minimum value at x 0 , then f '(x 0 ) = 0. In view of the above theorems, we state the following rul..

(First Derivative Test) Let f (x) be a real valued differentiable function. Let a be a point on an interval I such that f '(a) = 0. (a) a is a local maxima of the function f (x) if i) f (a) = 0 ii) f (x) changes sign from positive to negative as x increases through a. That is, f (x) > 0 for x &l..

Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..

If f and g are real functions such that fog is defined, if g is continuous at a point c, and if f is continuous at g(c), then fog is continuous at ..

Rolle's Theorem - Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..

The Derivative of Some Important Functions are: 1. Derivative of a Constant, 2. Derivative of x n where n is any integer, 3. Derivative of a Constant of a Function, 4. Derivative of Exponential Functio..

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieve..