Calc I Urgent!!

Question

The quantity, q, of a certain skateboard sold depends on the selling price, p, in dollars, so we write q = f(p). You are given that f(140) = 15400 and f '(140) = −60.

(a) What does f(140) = 15400 tell you about the sales of skateboards?
When the price of the skateboard is $_____, then________ skateboards will be sold.

What does f '(140) = −60 tell you about the sales of skateboards?
If the price increases from $140 to $141, the number of skateboards sold would increase or decrease by ________ roughly skateboards.

If the skateboards are currently selling for $140, what happens to revenue if the price is increased to $141?
The revenue would increase or decrease by roughly $__________.

Answer 1

a)

 

 

q = f(p)

 

15400 = f(140)

 

This means that the selling price of 15400 skateboards is $140.

 

 

f'(140)=-60     means that the quantity of skateboards decreases at a rate of 60 skateboards per dollar at the sale of $140.

 

 

Since f'(140) is the slope of the tangent line at p=140, we use the slope at this point as well as p=141.  Here are your two points:

 

(140, 15400) and (141, q₂)

 

The slope between these two points is -60.  Use that fact to find q₂.

 

(q₂ - 15400) / (141 - 140) = -60

 

q₂ - 15400 = -60

 

q₂ = 15400 - 60

 

q₂ = 15340

 

 

Take the difference between 15340 and 15400.