**How to find the slope of a tangent line at a point :**

Here we are going to see how to find the slope of a tangent line at a point.

We may obtain the slope of tangent by finding the first derivative of the curve.

If f(x) is the equation of the curve, then f'(x) will be its slope.

f'(x) = dy/dx = m (slope of tangent)

Let us look into some examples to understand the above concept.

**Example 1 :**

Find the equation of the slope of tangent to the parabola y^{2} = 12x at the point (3, 6)

**Solution :**

**Equation of the given curve is ****y ^{2} = 12x**

**2y (dy/dx) = 12 (1)**

**2y**** (dy/dx) = 12**

**dy/dx = 12/2y ==> 6/y**

**Slope of tangent at (3, 6) is**

** m = 6/6**

** m = 1**

**Hence the slope of the tangent line at the given point is 1.**

**Example 2 :**

Find the equation of the tangent to the parabola x^{2} + x − 2y + 2 = 0 at (1, 2)

**Solution :**

Equation of the given curve x^{2} + x − 2y + 2 = 0

2x + 1 - 2 (dy/dx) + 0 = 0

2 (dy/dx) = 2x + 1

dy/dx = (2x + 1)/2

Slope of tangent at (1, 2) :

dy/dx = (2(1) + 1)/2 = 3/2

Hence the slope of tangent at the given point (1, 2) is 3/2.

**Example 3 :**

Find the equation of the tangent to the hyperbola 9x^{2}- 5y^{2} = 31 at (2, -1)

**Solution :**

Equation of the given curve is 9x^{2}- 5y^{2} = 31

18 x - 10 y (dy/dx) = 0

10y (dy/dx) = -18 x

dy/dx = -18x / 10 ==> -9x/5

Slope of tangent at the point (2, -1)

m = -9(2)/5 ==> -18/5

Hence the slope of the tangent at the given point is -18/5.

After having gone through the stuff given above, we hope that the students would have understood "How to find the slope of a tangent line at a point"

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