__Geometrical interpretation of derivative :__

__Geometrical interpretation of derivative :__**Consider a function y = f(x) and points P(x _{1}, y_{1}) and Q(x_{2}, y_{2}) on it. As x_{1} changes to x_{2}, y_{1} becomes y_{2}. Average rate of change will be given by**

**(which is clearly the slope of line PQ).**

**As Q → P i.e. as x _{2} → x_{1} or Δx → 0,**

**the average rate of change Δy/Δx becomes the instantaneous rate of change represented by dy/dx and thus dy/dx represent the slope of the tangent at P.**

__Equation of Tangent and Normal__

__Equation of Tangent and Normal__**The derivative of a function y = f(x) represents the slope of the tangent to the curve at the general point (x, y).**

**Let y = f (x) be the given curve. We already know that dy/dx at any point lying on the curve would give us the slope of the tangent that can be drawn at that point.**

**Let (x _{1}, y_{1}) be any point on the curve, that means, y_{1} = f(x_{1}).**

**Now the slope of the tangent that can be drawn to the curve at (x _{1}, y_{1}) will be**

**Thus the equation of the tangent at (x _{1}, y_{1}) would be,**

**Similarly, the equation of the normal at (x _{1}, y_{1}) would be**

**provided that **

**Note: If x = g (t) , y = h (t)**

**then ,**

__Next Page → __Length of Tangent , Normal , Sub-tangent and Sub-normal