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# Tangent Line Formula

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'

 Related Calculators Equation of Tangent Line Calculator Calculator Tangent Inverse Tangent Calculator with Sine Cosine and Tangent

## Tangent Line Problems

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Some solved problems on tangent line are given below:

### Solved Examples

Question 1: Find the tangent line of the curve f(x) = 3x2 - 3 at x0 = 0 ?
Solution:

Given:
f(x) = 3x2 - 3
x= 0

f(x0) = f(0) = 3(0)2 - 3 = -3
f'(x) = 6x
m = f'(x0) = 6(0) = 0

The tangent line formula is,
y - f(x0) = m(x - x0)
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) = 5x2 + 17 at x0 = 2 ?
Solution:

Given:
f(x) = 5x2 + 17
x0 = 2

f(x0) = f(2) = 5(2)2 + 17 = 37
f'(x) = 10x
m = f'(x0) = 10(2) = 20

The tangent line formula is,
y - f(x0) = m(x - x0)
y - 37 = 20(x - 2)
y - 37 = 20x - 40
20x - y - 3 = 0

The tangent of the curve is,
20x - y - 3 = 0

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