Suppose that the cost of drilling x feet for an oil well is C=f(x) dollars, If you've already drilled 550 feet, estimate the cost of drilling an additional foot if f′(550)=1800

Answer 1

f ' (550) ≅ [ f(551) −f(550)] /( 551 -550)

f ' (550) ≅ f(551) −f(550)

1800 ≅ f(551) −f(550) Then the cost for drilling an additional foot is $ 1800

Answer 2

Nothing is said as to the nature of f(x). Therefore we can assume that it is linear.

If the rate of change, f'(x), is 1800 at 550 feet then the next foot shall cost $1800