Question

show that the function f(x) =logx÷x for x isnot equal to 0 is maximum at x = e

Answer 1

f'(x)= 1-log(x)/x^2

for f'(x)=0

1- log(x)=0

log(x)=1

x=e

to find out if this point is of minima or maxima find f''(x) if its value at x=e is -ve then x=e is the point of maxima

f'(x)= 1-logx/x^2

f''(x)= -x -2x(1-logx)/x^4

at x=e

f''(x)= -1/e^3 hence point of MAXIMA