The amount of revenue a company makes per day by selling x items is given by the function f(x) = 14x - 0.2x^2. How many items should be sold if the company wants to maximize their profit?

Usually when profit is involved, there is almost always a cost function to subtract from the revenue.
That is Profit = Revenue - Cost
Believe me, Max Revenue does not always equal Max Profit.
What if it costs 1.50 to make x?
At any rate, given:
Revenue =f(x) = 14x - 0.2x^2.
take derivative to find max revenue
R prime =R' = 14 - 0.4x
set R' to zero and solve for x
0.4x =14
x= 14/0.4
x=35
When we sale 35 items or when x =35, we have reached Max Revenue.
Maybe true in your case for max profit as well; hope this helps