# A each cd costs freds band 320 to make and the band

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a. Each CD costs Fred’s band \$3.20 to make and the band has fixed costs of \$230, write down the formulas for R(x), C(x), and P (x) (the revenue, cost and profit functions in dollars). Write each formula out in full. Do not use any abbreviations. b. Use nDeriv to determine the price that maximizes REVENUE. Write the answerwith all the decimal places the calculator gives. i.calculator answer: ii. Circle the equation you solved: c. Show by comparing function values that the price you found in part (b) maximizes the revenue. iii.Circle the calculator procedure you used: (d) Round the selling price from part (b) to the nearest penny and fill in the following table with the values when REVENUE is maximized (put unit in the second line). Note that demand must be a whole number.Selling PriceDemand Revenue Cost Profit(e) Use nDeriv to determine the price that maximizes PROFIT. Show your work especially any equations you solve and tell how you use the calculator. Write the answer with all the decimal places the calculator gives.calculator answer:f.Use the second derivative test to show that the answer in part (e) maximizes the profit. 2. Let h(x) = −x3+9x2−30x+20. Put this function into your calculator as Y1 and
check that Y1(2) = −12. a. Use derivatives and basic algebra to find the inﬂection point of the function h(x). Give the x and y coordinates of the inﬂection point. Show your work especially any equations you solve and how you solve them. b. Graph h(x) on your calculator over the interval −2 ≤ x ≤ 6 and sketch what you see. In your sketch, the inﬂection point should be clearly labelled. Write down the window settings you use. Use the graph to decide what kind of inﬂection point the graph has. Circle one of the following. i.Point of fastest increase ii. Point of slowest increaser iii.Point of fastest decrease In problems 1–6, find the indicated general antiderivative, i.e., evaluate the given integral.1. ∫ (15x4 − 9x2) dx 2. ∫ 1765 x dx 3. ∫ ( 2x4 3 + 2 √ x ) dx 4. ∫ (5e−1.2t + 31.4) dt 5. ∫ 3x+ 2 5 dx 6. ∫ d(√4x+ dx 3 ) dx