38: The graphs intersect when ln(x) = (1 − x)/x. This equation is not solvable agebraically, but we can guess one solution: x = 1. Since the graphs of both functions are strictly monotone for x > 0, there is no other interection.

Slopes of tangent lines are given by the derivative. For the above point one should get

How do you recognize whether the slopes are perpendicular?

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