A tangent line of any curve is a line that touches the curve at a point called the **point of tangency. **For a curve y = f(x), the tangent line at a point x = a on the curve is the line that passes through the point(a, f(a)) on the curve and also has a slope equal to f'(a).

The **Tangent Line Formula** of the curve at any point 'a' is given as,

Where,

f(a) is the value of the curve function at a point 'a'

m is the value of the derivative of the curve function at a point 'a'

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Equation of Tangent Line Calculator | Calculator Tangent |

Inverse Tangent | Calculator with Sine Cosine and Tangent |

Some solved problems on tangent line are given below:

### Solved Examples

**Question 1: **Find the tangent line of the curve f(x) = 3x^{2 }- 3 at x_{0} = 0 ?

** Solution: **

Given:

f(x_{}) = 3x^{2} - 3

x_{0 }= 0

f(x_{0}) = f(0) = 3(0)^{2} - 3 = -3

f'(x) = 6x

m = f'(x_{0}) = 6(0) = 0

The tangent line formula is,

y - f(x_{0}) = m(x - x_{0})

y + 3 = 0(x - 0)

y + 3 = 0

The tangent of the curve is,

y + 3 = 0

**Question 2: **Find the tangent line of the curve f(x) = 5x^{2} + 17 at x_{0} = 2 ?

** Solution: **

Given:

f(x) = 5x^{2} + 17

x_{0} = 2

f(x_{0}) = f(2) = 5(2)^{2} + 17 = 37

f'(x) = 10x

m = f'(x_{0}) = 10(2) = 20

The tangent line formula is,

y - f(x_{0}) = m(x - x_{0})

y - 37 = 20(x - 2)

y - 37 = 20x - 40

20x - y - 3 = 0

The tangent of the curve is,

20x - y - 3 = 0

Given:

f(x

x

f(x

f'(x) = 6x

m = f'(x

The tangent line formula is,

y - f(x

y + 3 = 0(x - 0)

y + 3 = 0

The tangent of the curve is,

y + 3 = 0

Given:

f(x) = 5x

x

f(x

f'(x) = 10x

m = f'(x

The tangent line formula is,

y - f(x

y - 37 = 20(x - 2)

y - 37 = 20x - 40

20x - y - 3 = 0

The tangent of the curve is,

20x - y - 3 = 0