How would I graph this?

Question

The cost of producing x units of a product is C = 60x + 1350. For one week management determined the number of units produced at the end of t hours during an eight-hour shift. The average values of x for the week are shown in the table.

(a) Use a graphing utility to fit a cubic model to the data. (Round your coefficients to three decimal places.)

(b) Use the Chain Rule to find dC/dt. (Round your coefficients to three decimal places.)

Answer 1

I would recommend you use desmos for this. Open up desmos and click the plus symbol in the upper left and select "table". Populate the table with the data using the "t" values as "x₁" data and the "x" values as "y₁" data to give you a table like this:

x₁ y₁

0 0

1 17

2 60

3 130

4 203

5 275

6 339

7 386

8 388

Then click on the plus symbol in the upper left hand corner again and this time select "f(x) expression". Enter y₁ ~ ax₁³ + bx₁² + cx₁ + d

To enter y₁, type y, then the underscore then the number 1 then to get out of the subscripting, use the cursor over button. The "~" is the button just left of the number 1 on your keyboard.

When finished you should get this:

You now have the values of a, b, c, and d for the function that models the data. The R² tells how good the fit is (with "1" being perfect). This is actually a really good fit at 0.9998.

You can now take the derivative using the power rule to get dx/dt. You can also take the power rule on C(x) to get dC/dx. Then dC/dt = dC/dx • dx/dt