If f(x)={e−∣x∣,−5<x<0−e−∣x−1∣+e−1+1,0≤x<2e−∣x−2∣,2≤x<4\text{If } f(x) = \begin{cases} e^{-|x|}, & -5 < x < 0 \\ -e^{-|x-1|} + e^{-1} + 1, & 0 \le x < 2 \\ e^{-|x-2|}, & 2 \le x < 4 \end{cases}…

Mathematics

Problem

If f(x)={e−∣x∣,−5<x<0−e−∣x−1∣+e−1+1,0≤x<2e−∣x−2∣,2≤x<4\text{If } f(x) = \begin{cases} e^{-|x|}, & -5 < x < 0 \\ -e^{-|x-1|} + e^{-1} + 1, & 0 \le x < 2 \\ e^{-|x-2|}, & 2 \le x < 4 \end{cases} Discuss the continuity and differentiability of f(x)f(x) in the interval (−5,4)(-5, 4) .

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