Question

A tangent is drawn on the curve of the function \( y = x^2 \) at the point \( (x, y) = (3, 9) \). The slope of the tangent is _______.

• A. 3
• B. 6
• C. 9
• D. 12

Hint:

The slope of the tangent to a curve is given by the derivative of the function at the point of interest.

Answer 1

The Correct Option is B

The slope of the tangent to a curve at any point is given by the derivative of the function at that point. The given function is \( y = x^2 \). Step 1: Find the derivative of the function.
The derivative of \( y = x^2 \) with respect to \( x \) is: \[ \frac{dy}{dx} = 2x. \] Step 2: Find the slope at \( x = 3 \).
Substitute \( x = 3 \) into the derivative: \[ \frac{dy}{dx} \bigg|_{x=3} = 2(3) = 6. \] Thus, the slope of the tangent at \( (3, 9) \) is 6. Final Answer: \[ \boxed{\text{(B) 6}}. \]