Nitai M. answered • 12/08/19

Experienced High School and College Tutor Specializing in STEM

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!