InterviewSolution
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InterviewSolution
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Tangent at `(1,e)` on the curve `y=xe^(x^2)`, also passes through the point (a) `((4)/(3),2e)` (b) `((5)/(3),e)` (c) `((4)/(3),3e)` (d) `((3)/(4),3e)`A. `((4)/(3),2e)`B. `(3,6e)`C. `(2,3e)`D. `((5)/(3),2e)` |
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Answer» Given equation of curve is `y=xe^(x^(2))` …..`(i)` Note that `(1,e)` lie on the curve, so the point of contact is `(1,e)`. Now, slope of tangent, at point `(1,e)` , to the curve `(i)` is `(dy)/(dx)|_(((1,e)))=(x(2x)e^(x^(2))+e^(x^(2)))_(((1,e)))` `=2e+e=3e` Now, equation of tangent is given by `(y-y_(1))=m(x-x_(1))` `y-e=3e(x-1)impliesy=3ex-2e` On checking all the options, the option `((4)/(3),2e)` satisfy the equation of tangent. |
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