2.6 The Chain Rule (GPR) - Practice

The Chain Rule (GPR) - Practice

Use the Chain Rule (GPR) to find the derivative of each function below.

Jimmy Crack Corn Inc

10) Jimmy Crack Corn Inc sells cracked corn. The company's cost function is

dollars, where x is the number of cracked corns made. Find the marginal cost function and evaluate it when 100 cracked corns have been produced.

Mutual Funds

11) Assume $5000 is invested into a mutual fund paying r% in returns annually. In 10 years its value will be

dollars. Find V'(12) and interpret your answer.

Tusky's Population

12) The population of Tusky x years from now is expected to be

hundred people for 1 < x < 5. Find P'(4) and interpret your answer.

Answers

Jimmy Cracked Corn Inc

10) MC(100) = $20.41 per cracked corn

When 100 cracked corns have been made, the cost to build the next cracked corn is $2.04.

When 100 cracked corns have been made, the total cost is increasing by $2.04 per cracked corn. 

Mutual Fund

11) V'(12) = $1386.54 per %

When the annual return is 12%, the mutual fund's value is increasing by $1386.54 per percentage.(This means you'd make $1386.54 more if your return was 13%)

Tusky's Population

12) P'(4) = 4/3 = 1.33 hundred people per year

Four years from now, Tusky's population will be growing by 133 people per year.