Tangent Line Calculator

Tangent Line Calculator is used to determine the equation of a tangent to a given curve. In geometry, a tangent is the line drawn from an external point and passes through a point on the curve. A tangent is a line or a plane that touches a curve or a curved surface at exactly one point.

What is Tangent Line Calculator?

Tangent Line Calculator is an online tool that helps to find the equation of the tangent line to a given curve when we know the x coordinate of the point of intersection. The point-slope form of a line can be used to find the equation of a tangent. To use the tangent line calculator, enter the values in the given input boxes.

Tangent Line Calculator

How to Use Tangent Line Calculator?

Please follow the steps given below to find the equation of the tangent line using the online tangent line calculator:

• Step 1: Go to online tangent line calculator.
• Step 2: Enter the values in the given input boxes.
• Step 3: Click on the "Calculate" button to find the equation of the tangent line.
• Step 4: Click on the "Reset" button to clear the fields and enter new values.

Hoes Does Tangent Line Calculator Work?

To determine the equation of a tangent, we need to know the slope of the line as well as the point where it touches the curve. If we take the first-order derivative of the given function and evaluate it at the point of intersection, we can find the slope of a tangent. Suppose we know the function of the curve, f(x), that the tangent touches and the x coordinate, x₁, of the point of intersection. Then we can follow the steps given below to find the equation of the tangent.

• Substitute the value of the x coordinate, x₁, in the given function f(x). This gives us the y coordinate, y₁, of the point of intersection.
• Differentiate the given function of the curve; f'(x).
• Substitute the value of the x coordinate in f'(x). This will give us the slope of the tangent.
• According to the point-slope form, the equation of a line passing through some point (x₀, y₀) with a slope m is given as y - y₀ = m (x - x₀).
• Thus, using this concept, the equation of a tangent can be given as y - y₁ = f'(x) (x - x₁). Substitute the values in this equation to find the tangent line equation.

Solved Examples on Tangent Line Calculator

Example 1:

Find the equation of the tangent line for the given function f(x) = 3x² at x = 2 and verify it using the online tangent line calculator.

Solution:

At x = 2, y = 3x²

Substituting the value of x in the above equation, we get

y = 3 × 2²

y = 12

Given: y = f(x) = 3x²

m = f '(x) = 6x

At x = 2

f'(2) = 6 × 2

f'(2) = 12

Equation of tangent line having slope f'(x) = 12 and passing through (2, 12) is

y - y₁ = f'(x)(x - x₁)

y - 12 = 12(x - 2)

y - 12 = 12x - 24

12x - y -12 = 0.

Therefore, the equation of the tangent line is 12x - y - 12 = 0

Example 2:

Find the equation of the tangent line for the given function f(x) = xln(x) at x = 1 and verify it using the online tangent line calculator.

Solution:

At x = 1, y = xln(x)

= 1 × ln(1)

= 0

Given: y = f(x) = xln(x)

m = f '(x) = ln(x) + x / x

f'(x) = lnx + 1

At x = 1,

f'(1) = 0 + 1 = 1

Equation of tangent line having slope f'(x) = 1 and passing through (1, 0) is

y - y₁ = f'(x)(x - x₁)

y - 0 = 1(x - 1)

x - y - 1 = 0

Therefore, the equation of the tangent line is x - y - 1 = 0

Similarly, you can use the tangent line calculator to find the equation of the tangent line for the following:

• y = e^xln(x) at x = 1.
• y = 5x³ + 1.2x at x = 3.

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• Tangent Line
• Tangent Function

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