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6. Suppose that the number of items sold after t months is modelled by 500t (25t + 2)² a. Find N'(6) and N'(12). b. Find N"(6), N"(12). c. What do the answers in a. and b. tell you about N(t)? N(t): =

6. Suppose that the number of items sold after t months is modelled by 500t (25t + 2)² a. Find N'(6) and N'(12). b. Find N"(6), N"(12). c. What do the answers in a. and b. tell you about N(t)? N(t): =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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6. 7. 8. Suppose that the number of items sold after t months is modelled by 500t (25t + 2)² a. Find N'(6) and N'(12). b. Find N"(6), N"(12). c. What do the answers in a. and b. tell you about N (t)? N(t) = Let f(x) = x+₁ and g(x) = √x. Let g(x) = √x and let x-1 h(x) = fo g. a. Find h'(x) b. Find h'(4) A company determines the cost, in thousands of dollars for producing x items is given by C(x) = √500x²-x + 75. Suppose that it plans to boost production in t months from now according to the function x(t) = 30t + 7. Use implicit differentiation to find how fast the cost will be rising 6 months from now.
Transcribed Image Text:6. 7. 8. Suppose that the number of items sold after t months is modelled by 500t (25t + 2)² a. Find N'(6) and N'(12). b. Find N"(6), N"(12). c. What do the answers in a. and b. tell you about N (t)? N(t) = Let f(x) = x+₁ and g(x) = √x. Let g(x) = √x and let x-1 h(x) = fo g. a. Find h'(x) b. Find h'(4) A company determines the cost, in thousands of dollars for producing x items is given by C(x) = √500x²-x + 75. Suppose that it plans to boost production in t months from now according to the function x(t) = 30t + 7. Use implicit differentiation to find how fast the cost will be rising 6 months from now.
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