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The tangent to the curve yt=xe^(x^2) pas...

The tangent to the curve `yt=xe^(x^2)` passing through the point (1,e) also passes through the point

A

(3, 6e)

B

`((5)/(3), 2e)`

C

`((4)/(3), 2e)`

D

(2, 3e)

Text Solution

Verified by Experts

The correct Answer is:
C
Tangent to the curve `y=xe^(x^(2))`
Point (1, e) lie on the curve
(Slope of tangent) `=(dy)/(dx)"|"_(1,e)=e^(x^(2))+xe^(x^(2)) xx 2x=e^(x^(2))(1+2x^(2))=e(1+2)=3e`
Equation of tangent
`(y-e)/(x-1)=3e`
`y=3xe-2e`
At `x=(4)/(3)`
`y=3xx(4)/(3)(e)-2e=2e`
We get `y=2e`
So this point `((4)/(3), 2e)` will lie on tangent
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