1.4 KiB
1.4 KiB
title |
---|
Equation of Tangent Line |
Equation of Tangent Line
A tangent line to a curve is a straight line that touches a curve, or a graph of a function, at only a single point. The tangent line represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point.
Finding Equation of the tangent line:
To find the equation of tangent line to a curve at point x=x0, we need to find the following:
- Find the derivative of the function (i.e.derivative of the equation of curve).
- Find the value of the derivative by putting x=x0 , this will be the slope of the tangent (say m).
- Find the value y0, by putting the value of x0 in the equation of the curve. Our tangent will pass through this point (x0,y0)
- Find the equation of the tangent using point-slope form. As the tangent passes through (x0,y0) and have slope m, the equation of the tangent line can be given as: (y-y0)=m.(x-x0)
Example : To find the equation of tangent line to the curve f(x) = 4x^2-4x+1 at x=1
Solution: f(x) = 4x^2-4x+1
Step 1 : f'(x) = 8x-4
Step 2 : m = f'(2) = 8.2-4 = 12
Step 3 : y0= f(x0) = f(2) = 4.2^2-4.2+1 = 16-8+1 = 9
Step 4 : m=12 ; (x0,y0)=(2,9)
Therefore, equation of tangent line is : (y-y0)=m.(x-x0)
=> (y-9)=12(x-2)
=> y=12x-15