A) \[\left( \frac{4}{3},\,\,\,2e \right)\]
B) \[\left( 3,\,\,\,6e \right)\]
C) \[\left( 2,\,\,3e \right)\]
D) \[\left( \frac{5}{3},\,\,2e \right)\]
Correct Answer: A
Solution :
\[\frac{dy}{dx}\,=\,{{e}^{{{x}^{2}}}}\,+\,x{{e}^{{{x}^{2}}}}\,.\,2x\] At \[x=1\], slope of tangent \[m=3e\] Equation of tangent: \[y-e=3e\left( x-1 \right)\] \[\Rightarrow \,\,\,y=3ex-2e\] \[\left( \frac{4}{3},\,\,2e \right)\] lies on it
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