Differentiation

Professor CalculusNew Topic: Differentiation, MiA Higher Ch3

By the end of this topic you will:
• be familiar with the terminology associated with differentiation
• understand the principles of differentiation
• be able to derive the gradient formula of a given function
• be able to calculate the gradient of a tangent to a curve
• be able to use differentiation to solve optimisation problems

22 Responses

  1. Thursday 9 September, period 2

    Introduction to Differentiation

    How can we determine the gradient of a curve?

    Beginning with linear travel graphs we will look at the parabolic path of a basketball to try and answer this question.

    Basketball Parabola

  2. Friday 10 September, period 5

    Differentiation from First Principles

    Differentiation from First Principles

  3. Monday 13 September, period 1

    Starter: Find the equation of the parabola below
    Find the equation of this parabola

    Recap ‘first principles’ lesson then use to differentiate some basic functions,
    e.g. f(x) = 3x, f(x) = x²

    Consolidate mental rule “Multiply by the power, take one from the power” – practice differentiating polynomial functions.

    Introduce practical experiment which will be carried out on Tuesday – calculating the gravitational constant.

    • There are times when we need to work faster.
      More of the class need to review a days work more often to allow us to progress effectively lesson to lesson.

      Too much time spent going over work covered on Friday.

      Practical lesson described, starter completed but not as much time as planned spent practicing finding derivatives.

      Class are to be prepared for practical lesson by ensuring they can find the equation of a parabola from its graph.

  4. Tuesday 14 September, period 4

    Practical experiment:
    Use a digital camera and softball to capture video of parabolic flight of a ball.

    Use Windows Movie Maker on laptops to freeze frame the videos and estimate height of ball for each frame (frame rate 4/100 sec)

    Plot on graph pa[er and determine equation of the parabola.

    Final task is to deduce how to determine an experimental value for the gravitational constant.

    • Best results were RS & DM with g = -9.6 m/s²

      Most results came in between -8 and -12.
      Variations were due to experimental error estimating position of the ball. Some pairs tried different values for a point on the curve and obtained different g values.

      Well done folks!

  5. Wednesday 15 September, periods 5 & 6

    Complete any unfinished gravity calculations. Recap by working through a class example.

    Practice differentiating various class created functions.

  6. Thursday 16 September, period 2

    Discuss Composite Functions homework.

    Revise and practice working with indices.
    In particular negative and fractional indices.

    Homework: Trig Functions
    Due: Thursday 23 September

  7. Friday 17 September, period 5

    Further practice differentiating functions.
    Focus on those with negative, fractional powers and with ‘sorting out’ to do before and after the differentiation step.
    Use selection from MiA p64-65 E4A & B

  8. is the homework the differentiation one? i cant remember and there are too many there to know what the homework is

  9. Monday 20 September, period 1

    Differentiation Functions Ex4B
    Continue to focus on negative/fractional indices and arranging function before and after differentiation step.

  10. Tuesday 21 September, period 4&

    Tangents to curves
    Start Ex5A

  11. Wednesday 22 September, periods 5 & 6

    Continue working on tangents to curves
    Complete Ex5A and Q1-4 from Ex5B

    Period 6 – Stationary Points Ex2

  12. Thursday 23 September, period 2

    Curve Sketching
    Start with a quadratic example and sketch using roots and line of symmetry, repeat by completing the square then finally by stationary points.

    Cubic example then start Ex3

  13. Friday 24 September, period 5

    Continue to practice full curve sketching sum.
    Aim for at least three completed in period.

  14. Worked solutions to Curve Sketching questions 9-11:

    Maths in Action p75 Q9

    Maths in Action p75 Q10

    Maths in Action p74 Q11

    Use these to check your solutions after you have tried them!

  15. Monday 27 September, period 1

    Check curve sketching examples completed at home.

    Optimisation Ex5A
    Cover Q1,5,6 as worked examples

    Reminder about homework procedures.

    Ask class to bring in tin can from kitchen cupboards for Tuesday’s lesson.

  16. Tuesday 28 September, period 4

    Applying optimisation to solve practical problem.

    “Are the tins in our kitchen cupboards the most efficient construction?”

    Use optimisation to deduce whether the tins use the optimal amount of metal.

  17. Wednesday 29 September, periods 5 & 6

    Period 5
    Baked Beans
    Applying optimisation to solve practical problem.

    “Are the tins in our kitchen cupboards the most efficient construction?”

    Use optimisation to deduce whether the tins use the optimal amount of metal.

    Period 6
    Introduction to Recurrence Relations
    Ex1-3 selected examples

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