1.Find the values of x where f(x)=2x² - x and g(x)=x²-4 have the same slope.

2.(20%) Assume the production cost (dollars/unit) for a manufacturing unit of a certain product is given by f (x) = 2(1+x) e^-x + 5 +250 where x is the number of units.

(a)Show that the marginal cost of the production will be increased to a certain value of x, and then decreasing from there on. You can consider x a continuous variable. For instance, it is alright to have x=0.1, partial unit of the product. In a practical application, you can always rounded your final calculated result in a whole unit (e.g., x=0.85 as x=1 unit). You can read the textbook (Sect. 2.1. Interpretation of the Derivative) for the definition of the marginal cost.

(b)Explain (no actual calculation is required) how you will determine at what level of production that will have the minimum marginal cost.