Mathematics

Problem

Let

p(x)=\ln x-\dfrac{x}{2}

be defined for

x>0

. a. (i) Determine all stationary points of

p(x)

for

x>0

." b. (ii) Classify each stationary point obtained in (i)." c. (iii) Using the information from (ii), find the greatest value of

p(x)

and hence state the range of

p

(0,\infty)