Piecewise Functions - 2

Calculus Level 3

f(x)={x3+2x2+x+c,if xbex,if x>b.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:RRf : \mathbb{R} \rightarrow \mathbb{R} be defined as the piecewise function above.

It is given that ff is differentiable for all real values of xx, and bb and cc are integers.

Find b+cb + c.

Clarification: ee denotes Euler's number, e2.71828e \approx 2.71828.

This problem is part of the set - Piecewise-defined Functions.

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