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g(x)=(\alpha+|x|)^{2}e^{(5-|x|)^{2}}

Source: Isi 2012 #2

May 13, 2012

functionlimitcalculusderivativecalculus computationsisi

Problem Statement

Consider the following function

g(x)=(\alpha+|x|)^{2}e^{(5-|x|)^{2}}

i) Find all the values of

\alpha

for which

g(x)

is continuous for all

x\in\mathbb{R}

ii)Find all the values of

\alpha

for which

g(x)

is differentiable for all

x\in\mathbb{R}