MathDB

2

Part of 2012 ISI Entrance Examination

Problems(1)

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

Source: Isi 2012 #2

5/13/2012
Consider the following function g(x)=(α+∣x∣)2e(5−∣x∣)2g(x)=(\alpha+|x|)^{2}e^{(5-|x|)^{2}} i) Find all the values of α\alpha for which g(x)g(x) is continuous for all x∈Rx\in\mathbb{R}
ii)Find all the values of α\alpha for which g(x)g(x) is differentiable for all x∈Rx\in\mathbb{R}.
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