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Question:

The tangent to the curve y = xex² passing through the point (1, e) also passes through the point: (2, 3e), (4/3, 2e), (5/3, 2e), (3, 6e)

(3,6e)

(43,2e)

(2,3e)

(53,2e)

Solution:

y = xex²
dy/dx |(1,e) = (x * ex² * 2x + ex²)|(1,e) = 2e + e = 3e
T: y - e = 3e(x - 1)
y = 3ex - 2e