Answer all the questions COMPLETELY. Vote will be given based on answers

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A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C = 0.4x2 + 7,000. How fast is the cost per month changing when production is changing at the rate of 17 units per month and the production level is 80 units? E) Costs are |:| at the rate of $ per month at this production level. (Round to the nearest dollar as needed.) The price p (in dollars) and demand x for wireless headphones are related by x = 8,000 - 0.15p2. The current price of $100 is decreasing at a rate $7 per week Find the associated revenue function R(p) and the rate of change (in dollars per week) of revenue R(P) = - (R(P)) = The rate of change of revenue is dollars per week. (Simplify your answer. Round to the nearest dollar per week as needed.)Use the price-demand equation x = f(p) = 1720 - 8p to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive.Demand is inelastic for all values of p in the interval (). (Type your answer in interval notation. Type integers or decimals.) Demand is elastic for all values of p in the interval (4). (Type your answer in interval notation. Type integers or decimals.)Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x. Find the value(s) of x where the tangent line is horizontal. f (x) = 7ex2 - 5x +8, x=0f'(x) = 51* V The equation of the line tangent to the graph of f at x = 0 is y = . Select the correct choice below and ll in any answer boxes in your choice. v The tangent line is horizontal at x: I . (Simplify your answer. Use a comma to separate answers as needed.) The tangent line is never horizontal. Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x. Find the value(s) of x where the tangent line is horizontal. f(x) = In (6 -x2 + 2x4); x=1f' ( x ) = The equation of the line tangent to the graph of f at x = 1 is y = Select the correct choice below and fill in any answer boxes in your choice. A. The value(s) of x where the tangent line is horizontal is/are (Simplify your answer. Use a comma to separate answers as needed.) X B. The tangent line is never horizontal.Use a graphing calculator to find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation y3 - xy - x5 = 4, where x = 1. Give the equation of the line that is tangent to the curve at x = 1. y =_ (Type your answer in slope-intercept form. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed. Round all intermediate values to two decimal places as needed.)