Question

If \(f(x) = \begin{cases} x^2 + 3x + a, & x \leq 1  bx + 2, & x>1 \end{cases}\), \(x \in \mathbb{R}\), 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 piecewise functions to be differentiable, ensure continuity and equal derivatives at the junction point by equating left and right limits and derivatives.