Question

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

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

Answer 1

Answer: (A)

$(\frac{4}{3},2e)$

$y=x{e}^{x^2}$

$\frac{dy}{dx}{|{}_{(1,e)}=(x\cdot e^{x^2}\cdot 2x+e^{x^2})|}_{1,e}=2\cdot e+e=3e$

$T:y-e=3e(x-1)$

$y=3ex-3e+e$

$y=\left(3e\right)x-2e$

Out of the options only option:A

$(\frac{4}{3},2e)$ lies on it as $2e=3e\times \frac{4}{3}-2e\Rightarrow 2e=2e$