Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. a. What does it mean to say that C(2000) = 800? b. What are the units of C'(r)? c. Suppose that C(2000) = 800 and C'(2000) = 0.35. Estimate C(2100), and justify your estimate by writing at least one sentence that explains your thinking. d. Do you think C'(2000) is less than, equal to, or greater than C'(3000)? Why?
Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. a. What does it mean to say that C(2000) = 800? b. What are the units of C'(r)? c. Suppose that C(2000) = 800 and C'(2000) = 0.35. Estimate C(2100), and justify your estimate by writing at least one sentence that explains your thinking. d. Do you think C'(2000) is less than, equal to, or greater than C'(3000)? Why?
Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. a. What does it mean to say that C(2000) = 800? b. What are the units of C'(r)? c. Suppose that C(2000) = 800 and C'(2000) = 0.35. Estimate C(2100), and justify your estimate by writing at least one sentence that explains your thinking. d. Do you think C'(2000) is less than, equal to, or greater than C'(3000)? Why?
Answer only option d. Please try not to use derivatives or integrals to calculate the stuff. Thank you.
Transcribed Image Text:Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet
of rope is C(r) dollars.
a. What does it mean to say that C(2000) = 800?
b. What are the units of C'(r)?
c. Suppose that C(2000) = 800 and C'(2000) = 0.35. Estimate C(2100), and justify
your estimate by writing at least one sentence that explains your thinking.
d. Do you think C'(2000) is less than, equal to, or greater than C'(3000)? Why?
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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