Question

If the normal to the curve \( y = f(x) \) at the point \( (3, 4) \) makes an angle \( 3\pi/4 \) with the positive x-axis, then \( f'(3) \) is:

• A. -1
• B. -3/4
• C. 4/3
• D. 3/4

Hint:

The slope of the normal is the negative reciprocal of the slope of the tangent. Use this to find the derivative at a point.

Answer 1

The Correct Option is C

Step 1: Use the slope of the normal.
The slope of the normal is the negative reciprocal of the slope of the tangent. The slope of the normal is given by \( \tan(3\pi/4) = -1 \), so the slope of the tangent is 4/3. Therefore, \( f'(3) = 4/3 \).
Thus, the correct answer is (3).