What is the value of q ?
For the next two (02) items that follow : Let \( f(x) = \begin{cases} ax(x-1), & x < 1 \\ x-1, & 1 \le x \le 3 \\ px^2 + qx + 2, & x > 3 \end{cases} \) Given that \( f(x) \) is continuous for all x but not differentiable at x = 1. Further \( f'(x) \) is continuous at x = 3.
- A. -1 ✓
- B. -\frac{1}{3}
- C. \frac{1}{3}
- D. 1
Correct Answer: A. -1
Explanation
From the continuity condition derived in the previous question, we have \( 3p + q = 0 \). Substituting \( p = 1/3 \) gives \( 3(1/3) + q = 0 \implies q = -1 \).
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