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can you help my for this 1. Chains Inc. is in the business of making and selling chains. Let c(t)be the number of miles of

can you help my for this

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1. Chains Inc. is in the business of making and selling chains. Let c(t)be the number of miles of chain produced after: hours of production. Let p(c) be the profit as a function of the number of miles of chain produced and let qft) be the profit as a function of the number of hours of production. Suppose the company can produce 3 miles of chain per hour and suppose their profit on the chains is $4DDD per mile of chain. Find and interpret [use complete sentences] each of the following {include units]. Cl) plfc). and q'(t). How does q'(t) relates to pl(c)and EH)? 2. Use Desmos to graph the function y3 + gm? + 3:2 333 = {I and estimate the slope of the tangent line at ['I,'l]. Then find 35 using implicit differentiation and plug in 3: = 1 and y = 1. Compare and discuss the estimated slope with the slope you found analytically. 3. Letf($) = (31:2 + 1)? Find f'[$) in 3 different ways by following the instructions below in parts ar b and c: a] Develop the identityf(s::l then take the derivative. b] View ffsj) as(3,r9 +1)(3;1:Q + 1) and use the product rule to nd f'($). c] Apply the chain rule directly to the expression f(3:) = (31:? + 1)? d] Are your answers in parts ar br c the same? 1li'il'hy or why not? 4. Find if? for the equation 31,-? _ cost: = $3

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