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The tangent to the curve, y = x e^(x²) passing through the point (1, e) also passes through the point

1. (4/3, 2e)
2. (3, 6e)
3. (2, 3e)
4. (5/3, 2e)

Correct answer: (4/3, 2e)

Solution

The tangent line at the point (1, e) on the curve has a specific slope determined by the derivative of the function at that point. By calculating the equation of the tangent line and checking which of the given points satisfies this equation, we find that (4/3, 2e) lies on the tangent line, confirming it as the correct option.

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