Question

1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr +1" has domain (-0,0). 6. [10 marks] Sketch the graph of y = -2 -2 log: (2-2) and find its domain, range, -intercept and y-intercept. Show your transformations step by step. 7. (12 marks] (a) [8 marks) Find the equation of the tangent line to the graph of the function f(x) = 3.0" - 6x2 - 7 at = 2 (b) (4 marks) Find the value(s) of where the tangent line to the graph of the function f(x) = 3.r* - 6.02 - 7 is horizontal. 8. [12 marks] The marketing research department for a company that manufactures and sells notebook computers established the following price-demand and revenue functions: Spa) = 2,000 - 50. R(x) = x2) Price-demand function Revenue function where p(x) is the wholesale price in dollars at which I thousand computers can be sold, and R(x) is in thousands of dollars. Both functions have domain 1<x< 30. (a) [4 marks) Sketch a graph of the revenue function in a rectangular coordinate system. (b) [6 marks) Find the value of that will produce the maximum revenue. What is the maximum revenue to the nearest thousand dollars? (c) 2 marks What is the wholesale price per computer that produces the maximum revenue?

Answer 1

fo) = ati To . . . Domain, 10 (-00,00) -*12+261 + define fol), Denominator of flu should not equals to zelo. –242 +264 +1 70 Tie possible only when. Discriminant, D <0 ie (2x)²-4X-1x1 <0. . = 4x² tu co K²+1 20 which is not possible such value of K Exist OR K = $ 1. So, No