The revenue function for a bicycle shop is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=800−0.5x is the unit price. Find the maximum revenue.

The maximum revenue is $320,000

Step-by-step explanation:

To find the maximum of a function f, the procedure is as follows:

The revenue function for a bicycle shop is

R(x)=xp(x), where p(x)=800-0.5x. Substituting:

Find the first derivative of R:

R'(x)=800-x

Equate to 0:

800-x=0

Solve:

x=800

There is only one critical point. Substitute it into the revenue function:

The maximum revenue is $320,000

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

c. (3,2,6) is the answer.