function and graph

Question

R(p)=-12p^2+1200p

find R when p=25.

find p and R for maximum R. 

Graph  R(p) when p>0

Answer 1

You should know how to evaluate a function at the independent variable.  So, I will guide you though the second and 3rd part.

 

You want the maximum R.  You need to find the p value that will give you the maximum R.

 

p = -b / (2a)

 

where:

a = -12

b = 1200

 

Plug in these values into the formula to find p. 

 

p = -(1200) / (2*-12)

p = 50

 

Then evaluate R(50) to get the maximum R.

 

 

 

Then to graph, you need several points:

x-intercepts, y-intercept, and vertex

 

 

To find x-intercept, set R(p) equal to zero and solve for p.

 

-12p² + 1200p = 0

 

-12p(p - 100) = 0

 

p = 0        or          p = 100

 

 

x-intercept = (0, 0) and (100, 0)

 

y-intercept = (0, 0)

 

vertex = (50, R(50))

 

 

Now that we have our points, we plot them.  Plot an open circle at (0, 0), a closed circle at (50, R(50)), and a closed circle at (100, 0).  Then connect the points in the order of those points.  The connection should also pass beyond the point (100, 0).