# Piecewise Functions - 2

Calculus Level 3

$f(x) = \begin{cases} x^3 + 2x^2 + x + c, & \text{if } x \leq b \\ e^x, & \text{if } x > b. \end{cases}$ 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.
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