Piecewise Functions - 2
Calculus
Level
4
\[f(x) = \begin{cases} x^3 + 2x^2 + x + c, & \text{if } x \leq b \\ e^x, & \text{if } x > b. \end{cases}\] Let a function \(f : \mathbb{R} \rightarrow \mathbb{R}\) be defined as the piecewise function above.
It is given that \(f\) is differentiable for all real values of \(x\), and \(b\) and \(c\) are integers.
Find \(b + c\).
Clarification: \(e\) denotes Euler's number, \(e \approx 2.71828\).
This problem is part of the set - Piecewise-defined Functions.
by
Pranshu Gaba