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Application of Derivatives

  • For a quantity y varying with another quantity x, satisfying the rule y = f(x), the rate of change of y with respect to x is given by  

The rate of change of y with respect to x at the point x = x0 is given by .

  • If the variables x and y are expressed in form of x = f(t) and y = g(t), then the rate of change of y with respect to x is given by
  1. A function f: (a, b) → R is said to be
  • increasing on (a, b), if x1 < x2 in (a, b)
  • decreasing on (a, b), if x1 < x2 in (a, b)

OR

If a function f is continuous on [a, b] and differentiable on (a, b), then

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