Tons of Toys produces and manufactures superhero action figures. Their total cost to produce x cases of superhero action figures is given by the cost function C(x), in thousands of dollars. The graph of C(x) is provided in the above applet (black curve) along with the graph of the Tons of Toys' marginal cost function C(x) (green curve). The tangent line to C(x) at A= Start point is also displayed. Use the applet to answer the following questions. Note that an input box is provided for you to enter a particular number of cases of superhero action figures. Also observe that the B= End point is one horizontal unit to the right of the Start point A (e.g., if A= Start point has x=1, then the B= End point has x=2 ). (a) Find the actual change in cost if Tons of Toys increases production from 11 cases of superhero action figures to 12 cases of superhero action figures by filling in the blanks: Actual Change in Cost =$$=$ This means the total cost increases by thousand dollars when production increased from 11 to 12 cases of Juperhero action figures. (b) Translate your answer in part (a) into function notation, using C(x). (c) Use Tons of Toys' marginal cost function, C(x) to complete the following: Whien Tons of Toys produces and manufactures 11 cases of superhero action figures, their costs are at an approximate rate of thousand dollars per case of superhero action figures produced. (d) Translate your answer in part (c) into function notation, using C(x). (e) Observe that your work in parts (a) to (d) Ilustrates the fact that C(n+1)C(n)+C(n) for n cases of action figures produced. In particular, C(11)+C(11)=andC(12)= are approximately equal to each other. Tons of Toys produces and manufactures superhero action figures. Their total cost to produce x cases of superhero action figures is given by the cost function C(x), in thousands of dollars. The graph of C(x) is provided in the above applet (black curve) along with the graph of the Tons of Toys' marginal cost function C(x) (green curve). The tangent line to C(x) at A= Start point is also displayed. Use the applet to answer the following questions. Note that an input box is provided for you to enter a particular number of cases of superhero action figures. Also observe that the B= End point is one horizontal unit to the right of the Start point A (e.g., if A= Start point has x=1, then the B= End point has x=2 ). (a) Find the actual change in cost if Tons of Toys increases production from 11 cases of superhero action figures to 12 cases of superhero action figures by filling in the blanks: Actual Change in Cost =$$=$ This means the total cost increases by thousand dollars when production increased from 11 to 12 cases of Juperhero action figures. (b) Translate your answer in part (a) into function notation, using C(x). (c) Use Tons of Toys' marginal cost function, C(x) to complete the following: Whien Tons of Toys produces and manufactures 11 cases of superhero action figures, their costs are at an approximate rate of thousand dollars per case of superhero action figures produced. (d) Translate your answer in part (c) into function notation, using C(x). (e) Observe that your work in parts (a) to (d) Ilustrates the fact that C(n+1)C(n)+C(n) for n cases of action figures produced. In particular, C(11)+C(11)=andC(12)= are approximately equal to each other
