To find the minima and maxima of a function, we should find the first derivative of the function, set it equal to zero, and solve for values of x.
R' = 198x - 0.18x^2
0 = 198x - 0.18x^2
0 = x(198 - 0.18x)
198 - 0.18x = 0 or x = 0
198 = 0.18x
x = 1100
Now we need to check that this is a relative maximum. First, we find the second derivative of the function:
R'' = 198 - 0.36x
At the point we are interested in examining (x = 1100), R'' is negative, which tells us that the graph opens down at this point. In other words, this point is relative maximum.
Hope this helps!
