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* = *x*_{0} 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

- A function
*f*:*a*,*b*) →**R**is said to be

- increasing on (
*a*,*b*), if*x*_{1}<*x*_{2}in (*a*,*b*) - decreasing on (
*a*,*b*), if*x*_{1}<*x*_{2}in (*a*,*b*)

**OR**

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

*f*is increasing in [*a*,*b*], if for each*x*Î (*a*,*b*)*f*is decreasing in[*a*,*b*], if for each*x*Î (*a*,*b*)*f*is constant function in*a*,*b*], if f…

To view the complete topic, please