Calculus Question

Question

Find the points at which y=f(x)=2x−ln(6x) has a global maximum, a global minimum, and a local, non-global maximum on the interval .1≤x≤2.7. Round your answers to two decimal places. 

Global Minimum: 

(x,y) = (_,_)

Global Maximum: 

(x,y) = (_,_)

 

 Local, Non-Global Maximum: 

(x,y) = (_,_)

 

Answer 1

By the EVT, these extrema will be located at x = .1 , x = 2.7 , or at any critical pts for f on the interval.

f(.1) = .71 , f(2.7) = 2.62

f^'(x) = 2 - 1/x = 0 , x = 1/2 , with f^' going from - to + there, so f(1/2) = -.10 a global min

Global max on [.1 , 2.7] at (2.7, 2.62). Local max on [.1 , 2.7] at (.1, .71). Global min on [.1 , 2.7] at (.5, -.10).