JEE PYQ: Application Of Derivatives Question 74
Question 74 - 2019 (10 Jan Shift 2)
The tangent to the curve $y = xe^{x^2}$ passing through the point $(1, e)$ also passes through the point:
(1) $(2, 3e)$
(2) $\left(\frac{4}{3}, 2e\right)$
(3) $\left(\frac{5}{3}, 2e\right)$
(4) $(3, 6e)$
Show Answer
Answer: (2)
Solution
At $x = 1$: $y = e$. $\frac{dy}{dx} = e^{x^2}(1 + 2x^2)$. At $x=1$: slope $= 3e$. Tangent: $y - e = 3e(x-1) \Rightarrow y = 3ex - 2e$. At $x = \frac{4}{3}$: $y = 4e - 2e = 2e$. So $\left(\frac{4}{3}, 2e\right)$.
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