(Q17) questions

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DO NOT USE the derivative of the polynomial functions to solve the question # 3!

12. Given the function y = log, x and its graph, complete the following: a) 2- S 55 .2 MHF 4UB Unit IV Workbook 14 b) Draw the secants from the point (4, 2) to each of the points on the curve ending at x = 1, 3, 3.5, 3.9, 3.99, 3.999.C) Determine the equations of each of the secants constructed in b) by completing the following chart. m =- Ay y = m(x-p)+4 Ax 4 2 c) Determine the equation of the tangent at (4,2) in simplified form. 13. a) Answer the following questions, given the function y = sin x.b) Draw the secants from the point (" ,1) to each of the points on the curve ending at x=0, 4 2 2 5x 6' 4 3 12 c) Determine the equations of each of the secants constructed in b) by completing the following chart. I, M =- Ay y = m(x-p)+q AT d) Determine the equation of the tangent at (- ,1) in simplified form. 14. Find the slope of the tangent to the function y= x -3x at the point (4, 4) using a point nearby and not using a table of values.15. Find the equation of the tangent to the function y = at\" 3x at the point {4. 4}. MHF 4UB Unit IV Workbook 9 Lesson 17 Workbook Properties of the Tangent to a Curve Support Questions 7. Determine the equation of a straight line that passes through the points (1, 5) and (-1, -2). B. A golf ball lying on the grass is hit so that its initial velocity is 2.5 m/s. The height, h, in metres, of the ball after t seconds can be modelled by the quadratic function h(/) = -4.917 +2.5t. Find the average rate of change for the interval Ists2.MHF 4UB Unit IV Workbook 10 9. The population of Canada was approximately 32 million in January 2006, with an annual growth rate of 5.4%. a) State the equation that predicts Canada's population on January 1 at any year in the future. b) At the current rate of population growth, by how much would you expect Canada's population to grow from January 1, 2007, to January 1, 2017? What is the average annual rate? c) By how much would you expect Canada's population to grow from January 1, 201.6, to January 1, 2017? What is the average annual rate? d) Explain why the rates you found in parts b) and c) are different.MHF 4UB Unit IV Workbook 11 10. An object is dropped from a height of 80 m. Its height above the ground is given by h = -5+ +80 where t is in seconds and h is in metres. a) When does the object hit the ground? b) What is its average velocity? c) Why is the velocity negative? d) What is the average velocity of the object during its last second? e) Why are your answers to parts b) and d) different?f) Complete the following table to determine the instantaneous velocity of the object as it hits the ground. Time Period Average Velocity Between t = 3 and t=4 seconds Between t = 3.9 and 1=4 seconds Between t = 3.99 And t = 4 seconds Between t =3.999 And t = 4 seconds The instantaneous velocity at t = 4 seconds is 11. Given the function y = 2* and its graph, complete the following: a) Coi'llb) Draw the secants from the point (0,1) to each of the points on the curve ending at x = 2, 1, 0.5, 0.1, 0.01, 0.001. MHF 4UB Unit IV Workbook 13 c) Determine the equations of each of the secants constructed in b) by completing the following chart. L Ay y = mx+ b m = AX d) Determine the equation of the tangent at (0, 1) in simplified form