Inverse functions

Question

At a particular location, f(p) is the number of gallons of gas sold when the price is p dollars per gallon.

(a) What does the statement f(1) = 4090 tell you about gas sales?

When the price is $1 per gallon, gallons 4090 of gas are sold.

(b) Find and interpret f^-1 (4090).

4090 gallons are sold when the price is $1 per gallon.

(c) What does the statement tell you about gas sales?

If the price increases from $1 per gallon, the sales decrease at a rate of 1053 gallons per $1 increase in price.

(d) Find and interpret (f^-1)' (4090). Where necessary, round to five decimal places.

When 4090 are already sold, sales decrease at the rate of one gallon per price increase of ______ dollars

I have already solved all of them except part d, based off my answers please help me solve for part d. I am on my last attempt and I have tried the answers (-0.0009, -0.0009506, and 0.0009506) Thank you

Answer 1

d) 4090-1053 = 3037 gallons sold at $2 per gallon, as price rises from $1 to $2 per gallon

1/3037 = .000032927

one gallon less purchased as price rises $.00032927

round to five decimal places: $.00033