calculus 1 homework question Absolute min and max question

Question

Find the absolute minimum and maximum values of 𝑓(𝑥)=𝑥−ln𝑥 over the interval [1/2,3]. 

Answer 1

f'(x) = 1 - 1/x = 0; x = 1

f(1/2) = 1/2 - ln(1/2) = 0.5 + ln2 = 1.193

f(1) = 1 (absolute min)

f(3) = 3 - ln3 = 1.9 (abs max)