GATE 2025 CS (CS1) – Question 31
Consider the given function $f(x)$.
$f(x) = \begin{cases} ax + b & \text{for } x < 1 \\ x^3 + x^2 + 1 & \text{for } x \ge 1 \end{cases}$
If the function is differentiable everywhere, the value of $b$ must be ________. (rounded off to one decimal place)
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Correct answer: -2.0
Explanation
Continuity at x=1 gives a+b=3. Matching derivatives gives a=3(1)^2+2(1)=5. So b=3-5=-2.