Business Calculus

Q1

Find f'(x) and find the equation of the line tangent to the graph of fat x = 2. f(x) = (1 + 4x)(5 - 2x) f' (x )Find f (x) and find the equation of the line tangent to the graph of fat x = 1. x - 6 f(x) = 7x - 1 f' (xx ) =Find f' (x) in two ways: (1) using the product rule and (2) simplifying first f( x ) = x (x - 3) Which of the following shows the result of using the product rule? O A. f'(x) = (x) (x - 3) '+ (x - 3) (x)' O B. F'(x) = (x ) (x' -3)'(x7 -3) (x5 )' O C. F(x )= (x5 ) (x8 )'+ (x -3) (x7 -3)' OD. F(x) = (x6 ) (x7 - 3)' - (x7 -3) (x8 )" O E. f'(x) = (x)'(x - 3) OF. F'( x ) = (*B )' + (x7 -3)The total sales of S (in thousands of DUD's) of a certain movie are given by the following formula where t is the number of months since the release of the DVD. Use the formula to answer the questions. 4Dt2 3+1er SE1}: 3) Find srru. S'ru = D According to economic theory, the demand x for a quantity in a free market dx decreases as the price p increases (see the figure). Suppose that the number x (A) Find dp of DVD players people are willing to buy per week from a retail chain at a price of 8,000 dx $p is given by x = 0.3p + 1: 10=ps70. dp S Answer parts (A), (B), and (C). 4000- X Demand 2000- 8,000 X= 0.3p + 1 40 80 Price (dollars)