Theorem 1:
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..Application of Derivatives Introduction
Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a he..
Application of Derivatives Animation
Application of Derivatives Animation..
Application of Derivatives Animation..Step1:
We know that every polynomial function is continuous and product of continues functions are continuous. f (x), being product of polynomials of degree 1, is a continuous function in [4,10..
Step 1:
Show the function f (x) is continuous on the closed interval [a, b..
Step 1
For a differentiable function f (x), find f '(x). Equate it to zero. Solve the equation f '(x) = 0 to get the Critical values of f (x..
Step 1:
Show that the function is continuous in the given interval. Some known standard functions which are continuous, can be mentioned directl..
Note 1:
The area bounded by the curves f(x) and g(x) and the ordinates x = a and x = b is given by ..
The area bounded by the curves f(x) and g(x) and the ordinates x = a and x = b is given by ..Example 1:
Form a differential equations by eliminating 'a' from the family of curves y 2 =4a..
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