Question

The equation of all lines having slope 2 which are tangent to the curve \( y = \frac{1}{x - 3} \), is

• A. \( y = 2 \)
• B. \( y = 2x \)
• C. \( y = 2x + 3 \)
• D. None of these

Hint:

To find the equation of a tangent line, first calculate the derivative of the curve and set it equal to the desired slope. Then solve for the equation of the tangent.

Answer 1

The Correct Option is D

Step 1: Find the derivative of the curve.
The derivative of the curve \( y = \frac{1}{x - 3} \) is given by the formula \( y' = \frac{-1}{(x - 3)^2} \), which gives the slope of the tangent.
Step 2: Use the tangent slope condition.
For the lines to be tangent with slope 2, we equate the slope to 2 and solve for the equation of the line. Final Answer: \[ \boxed{\text{None of these}} \]