Derivative
The derivative measures the instantaneous rate of change of the function , as distinct from its average rate of change . It is defined as the limit of the average rate of change in the function as the length of the interval on which the average is computed tends to zero .
Want to find instantaneous speed of car at a given point of time ? Use derivative . Derivative is used by Rocket Scientists to compute the precise velocity with which the satellite needs to be shot out from the rocket . Financial institutions need to predict the changes in the value of a particular stock knowing its present value
Numerical : Find the derivative at x = 2 of the function f ( x ) = 3x Solution :
f ’( 2 ) = lim hà0 [ f ( 2 + h ) - f ( 2 )] / h = lim hà0 [ 3 *( 2 + h ) – 3 * 2 ]/ h = lim hà0 ( 6 + 3h -6 )/ h = 3