Thread: functions increasing but product of two are not?

Show that both f(x) =x and g(x)=x-1 are strictly increasing on I =[0,1], but their product fg is not increasing on I

Originally Posted by gixxer998

Show that both f(x) =x and g(x)=x-1 are strictly increasing on I =[0,1], but their product fg is not increasing on I

It looks like you can show this with basic derivative properties. Show f and g have a positive slope on the interval first. Then take the product and differentiate. You should get a critical point in the interval of [0,1]