Find critical point of interval problem

[tronter]

Can you just say that $$x(4-x) <4$$ for $$x \in (0,2)$$? You don't need to prove this?

Or to prove this, just find critical point which is $$x = 2$$?

 

[statdad]

Two ways - you can choose.
1) Find the places where the left side is zero, pick a value of $$x$$ from each of the portions of the number line, and check whether the (left side - 4) is positive or negative at each location.
2) Note that in $$(0,2)$$ both factors on the left are smaller than two, so...