Question Detail

To find the maximum value of the function y = ln x / x (assuming 'log' means natural logarithm), we need to find the critical points by setting the first derivative to zero.Using the quotient rule (u/v)' = (u'v - uv') / v2, where u = ln x and v = x:u' = 1/xv' = 1dy/dx = [(1/x) * x - ln x * 1] / x2 = (1 - ln x) / x2.Set the derivative to zero to find critical points:(1 - ln x) / x2 = 0This implies 1 - ln x = 0, so ln x = 1.Solving for x, we get x = e.To confirm this is a maximum, we can use the first derivative test (checking signs around x=e) or the second derivative test. The first derivative changes from positive to negative at x = e, indicating a local maximum.Option D is 'e'.