A) \[(2,3e)\]
B) \[\left( \frac{4}{3},2e \right)\]
C) \[\left( \frac{5}{3},2e \right)\]
D) \[(3,6e)\]
Correct Answer: B
Solution :
\[y=x{{e}^{{{x}^{2}}}}\] |
\[(1,e)\]lies on this |
Now, \[\frac{dy}{dx}=x{{e}^{{{x}^{2}}}}.2x+{{e}^{{{x}^{2}}}}.1\] |
Put \[x=1\] |
\[m=2e+e=3e\] |
Equation of tangent at \[(1,e)\] |
\[y-e=3e(x-1)\] |
\[y-e=3ex-3e\] |
\[y=3ex-2e\] |
\[\left( \frac{4}{3},2e \right)\]satisfies it |
\[\therefore \]Answer is B. |
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