Tangent Using Differentiation





In this page tangent using differentiation we are going to see the how to find equation of tangent using the concept differentiation.

Procedure of finding equation of tangent using differentiation :

Step 1 : Differentiate the given equation of the curve once. If we differentiate the given equation we will get slope of the curve that is slope of tangent drawn to the curve.

Step 2 : We have to apply the given points in the general slope to get slope of the particular tangent at the particular point.

Step 3 : Now we have to apply the point and the slope in the formula

(y - y₁) = m (x - x₁)

Now we are going to see some example problems to understand this concept.

Example 1:

Find the equation of tangent to the curve y = x³ at the point (1,1)

Solution:

y = x³

Step 1 : Differentiate the equation of the curve once to find the slope of the curve that is slope of the tangent drawn to the curve.

      dy/dx = 3 x²

slope of the curve at the point (1 , 1)

  dy/dx = 3 (1)²

slope of the curve at the point (1,1) dy/dx = 3

Equation of the tangent:

(y - y₁) = m (x - x₁)

(y - 1) = 3 (x - 1)

 y - 1 = 3 x - 3

 3 x - y - 3 + 1 = 0

 3 x - y - 2 = 0


Example 2:

Find the equation of tangent to the curve y = x² - x - 2 at the point (1,-2)

Solution:

y = x² - x - 2

Step 1 : Differentiate the equation of the curve once to find the slope of the curve that is slope of the tangent drawn to the curve.

      dy/dx = 2 x - 1

slope of the curve at the point (1 , -2)

  dy/dx = 2 (1) - 1

           = 2 - 1

           = 1

slope of the curve (dy/dx) = 1

Equation of the tangent:

(y - y₁) = m (x - x₁)

(y - (-2)) = 1 (x - 1)

 y + 2 = x - 1

 x - y - 2 - 1 = 0

 x - y - 3 = 0

 tangent using differentiation