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