6 Calculus 101 Questions

1.

The limit represents the derivative of some function fat some number a. State such an f and a. 4\\./1t.+h2 Iim {130 h f00=Wa a=2 f(x)=4\\/)_(, 3:16 f(X)=v'_x: B=4 f(x)=x4, a=2 f(x)=\\/;, 3:16 A roast turkey is taken from an oven when its temperature has reached 185F and is placed on a table in a room where the temperature is 75 F. The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour. OF/min T (F) 200 P 100 0 30 60 90 120 150 t (min)The cost of producing x ounces of gold from a new gold mine is C : f(x) dollars. (a) What is the meaning of the derivative f'(x)? What are its units? PO!) is the average production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. f'(X) is the total amount of gold produced. Its units are ounces. PO!) is the total production cost. Its units are dollars. 1"(X) is the rate of change of the production cost with respect to the number of ounces of gold produced. Its units are dollars per ounce. (b) What does the statement f'{700) = 14 mean? After 14 ounces of gold have been produced, the average production cost is $700/ounce. So the cost of producing 14 ounces is about $700/ounce. After 700 ounces of gold have been produced, the rate at which the production cost is increasing is $14/ounce. So the cost of producing the 700th (or 7015t) ounce is about $14. The total cost to produce 14 ounces of gold is approximately $700. After 700 ounces of gold have been produced, the average production cost is $14founce. So the cost of producing 700 ounces is about $14lounce. (c) Do you think the values of f'(x) will increase or decrease in the short term? What about the long term? Explain. ---Selecl-- due to largescale operations. In the short term, the values of f'(x) wili because more efficient use is made of startup costs as X increases. But eventually f'(X) might I The graphs of four derivatives are given below. Match the graph of each function in (a)-(d) with the graph of its derivative in I- IV. The derivative represents the slope of the tangent to the function. Only one of the function graphs (a)(d) has just one horizontal tangent. This is graph . Skip {you cannot come back) Trace or copy the graph of the given function 1'. (Assume that the axes have equal scales.) Then use the method of this example to sketch the graph off ' below it. )7 _,___...._.-v- Trace or copy the graph of the given function 3'. (Assume that the axes have equal scales.) Then use the method of this example to sketch the graph off ' below it. Lie ,, s % a? %<