Question

Trying to check my test answers:
The cost of the producing x number of sandwiches is given by c(x) = y.
Complete the sentences using proper grammar.
a. The statement that c(50)=250 means that:

b. The statement that c'(50)=2 means that:

c. The average cost of producing one sandwich at this point is:

d. Estimate the cost of producing 51 sandwiches:


My answers:
a. if the costs is in dollars, it costs $250 to produce 50 sandwiches.
b. skipped, no idea of this answer.
c. $5
d. $255

What i really need to know is why i missed 'd.'
and if it wouldnt take long to explain how to get the answer for 'b.'

Answer 1

Your cost function is not a straight line
that means at different x's it goes up faster (or slower)
we use the derivative to tell how fast the cost (per sandwich) is changing

in this case, when making 50 sw's, it costs $2 to make 1 more sw
(that is what ( b ) means)

Answer 2

( b) is the "instantaneous" "change in cost"
( c) is the "average" change in cost

maybe this short video explains it
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/average-rate-of-change/v/average-rate-of-change-example-1

Answer 3

thanks phi, ill watch that video asap