Question

The tangent to the curve, $y=x{e}^{x^2}$ passing through the point $(1,e)$ also passes through the point :

• A. $(2,3e)$
• B. $(3,6e)$
• C. $(\frac{4}{3},2e)$
• D. $(\frac{5}{3},2e)$

Answer 1

The correct option is C $(\frac{4}{3},2e)$

Given curve, $y=x{e}^{x^2}$
And its slope of tangent $=\frac{dy}{dx}$
$\frac{dy}{dx}=x\cdot 2x\cdot e^{x^2}+e^{x^2}$
$=2x^2{e}^{x^2}+e^{x^2}$
$=e^{x^2}(1+2x^2)$
At point $(1,e),\frac{dy}{dx}=3e$
For given point $(1,e)$ equation of the tangent is
$(y-e)=3e(x-1)$
Hence, the point $(\frac{4}{3},2e)$ lies on the above line.