Find the equation of the tangent line to the curve at the point (1,𝑟(1))(1,r(1)).

𝑦=

To find the equation of the tangent line to the curve at the point \( (1, r(1)) \), we need to follow these steps:

### Step 1: Identify the curve
You have not provided the equation of the curve \( y = r(x) \). Could you clarify what function \( r(x) \) is? For example, is it a specific function like \( r(x) = x^2 \) or something else?

### Step 2: Use the formula for the equation of the tangent line
The general form of the equation of the tangent line at a point \( (x_1, y_1) \) on the curve is:

\[
y - y_1 = m(x - x_1)
\]

where:
- \( (x_1, y_1) = (1, r(1)) \)
- \( m \) is the slope of the tangent line, which is the derivative \( r'(x) \) evaluated at \( x = 1 \).

### Step 3: Find the derivative
To find the slope of the tangent line, we need to compute the derivative \( r'(x) \). If you can provide the equation for \( r(x) \), I can help you find the derivative.

Once I have the derivative, I can plug in \( x = 1 \) to get the slope \( m = r'(1) \).

### Step 4: Write the equation of the tangent line
Using the values \( m = r'(1) \) and \( y_1 = r(1) \), I will plug them into the tangent line equation to give you the final result.

Please provide the function \( r(x) \) so I can continue!

Find the equation of the tangent line to the curve at the point (1, r(1)).

Learn how to find the equation of the tangent line to a curve at the point (1, r(1)). This problem involves key calculus concepts, such as derivatives and tangent lines, and is suitable for students in Grades 11-12.

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