Calculus Bagel Question

Question

In this question, I already got part a) but I'm having trouble with b & c.

The dollar cost of producing 𝑥 bagels is 𝐶(𝑥)=300+0.25𝑥−0.5(𝑥/1000)^3.

a) Determine the cost of producing 1000 bagels.

c(1000)=$549.5

b) Estimate the cost of the 1001st bagel.

c) Find the actual cost of the 1001st bagel.

Answer 1

Hi Heather,

We want to approximate the cost function near x=1000 with a straight line. We can use the slope of the tangent line to calculate the slope of our line. y-y0=m(x-x0) where y0=549.5 and x0=1000 and m=dC/dx

dC/Dx=.25-.5*3*(x/1000)²*1/1000=.25-.0015*(x/1000)² When we evaluate this at x=1000 we get m=.2485

So the cost of the 1001 st bagel is y-y0=.2485 *1 or $.25

To find the actual cost you just calculate the cost of 1001 bagels and subtract the cost of 1000 bagels ($549.5)

Regards

Jim