Fill This Form To Receive Instant Help

Help in Homework
trustpilot ratings
google ratings


Homework answers / question archive / Sir Arthur Lewis Community College MAT109 CALCULUS ASSIGNMENT – DIFFERENTIATION Assignment Three   The curve C has equation  3    8                                                                 ? =        ?3 − 9?2 +        + 30, ? > 0 ? Find ??

Sir Arthur Lewis Community College MAT109 CALCULUS ASSIGNMENT – DIFFERENTIATION Assignment Three   The curve C has equation  3    8                                                                 ? =        ?3 − 9?2 +        + 30, ? > 0 ? Find ??

Math

Sir Arthur Lewis Community College

MAT109 CALCULUS ASSIGNMENT – DIFFERENTIATION

Assignment Three

 

  1. The curve C has equation 
      1. 3    8

                                                                ? =        ?3 − 9?2 +        + 30, ? > 0

      1. ?
    1. Find ?? .                                                                                                                               [4]

??

    1. Show that the point ?(4, −8) ???? ?? ?.                                                                  [2]
    2. Find an equation of the tangent to C at the point ?, giving your answer in the ???? ?? + ?? = ? = 0 ????? ?, ? ??? ? are integers to be determined 

                             [6]

 

 

  1. A curve C has equation            ? = −2?3 + 3?2 + 12 − 5

??

    1. Find (i)                                                                                                                                [3]

??

?2?

                               (ii) 2                                                                                                                                                [2]

??

    1. Verify that C has  stationary points  at ? = 2 ??? ? = −1                                    [6]

              ( c) Determine the nature of the stationary points of C                                                                                                                                                                                                              [4]

 

 

  1. A rectangular box with a square base, an open top, and a volume of 96?3 is to be constructed. What should the dimensions of the box be to minimize the surface area of the box? What is the minimum surface area?                                                               [8]

 

  1. Sketch the graph of the curve ? = ?4 − 4? + 10                                                                 [7]

 

 

  1. The length ? of a rectangle is decreasing at the rate of 4 cm/s and the width ? is increasing at the rate of 5cm/s. When ? = 8   ???  ? = 6 find the rate of change of
    1. perimeter and (b) are of the rectangle.                                                                    [8]

 

 

  1. The volume of a cube is increasing at a rate of 9??3/?. How fast is the surface area

              increasing when the edge is 12cm?                                                                                                                                                 [6]

 

Total 50 marks

Purchase A New Answer

Custom new solution created by our subject matter experts

GET A QUOTE