Let h(x)={2x+1,x<0,x2,x≥0,andH(x)=∫0h(x)et2 dt.h(x)=\begin{cases}2x+1, & x<0,\\ x^{2}, & x\ge 0,\end{cases}\quad \text{and}\quad H(x)=\int_{0}^{h(x)} e^{t^{2}}\,dt.…

Mathematics

Problem

Let h(x)={2x+1,x<0,x2,x≥0,andH(x)=∫0h(x)et2 dt.h(x)=\begin{cases}2x+1, & x<0,\\ x^{2}, & x\ge 0,\end{cases}\quad \text{and}\quad H(x)=\int_{0}^{h(x)} e^{t^{2}}\,dt. Which statement about the differentiability of HH at x=0x=0 is correct? a) HH is differentiable at 00 and H′(0)=0H'(0)=0. b) HH is differentiable at 00 and H′(0)=2eH'(0)=2e. c) HH is not differentiable at 00. d) HH is differentiable at 00 and H′(0)=1H'(0)=1.

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