Question

Question:
If \[ f(x) = \begin{cases} x^2 + 3x + a, & x \le 1 \\ bx + 2, & x > 1 \end{cases} \] for \( x \in \mathbb{R} \), and the function is everywhere differentiable, then:

• A. \( a = 3, b = 5 \)
• B. \( a = 0, b = 5 \)
• C. \( a = 0, b = 3 \)
• D. \( a = b = 3 \)

Hint:

For differentiability of piecewise functions: First ensure continuity. Then match left and right derivatives. Always check the junction point.

Answer 1

The Correct Option is C