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CALcuLus

CALcuLus. How do you know how fast You are going? . “well how do you know How fast you’re going Right now, At this very second?” . Push your friend so that his/her speed changes Try to measure their speed at any single point. Paper darts. Create your own paper dart.

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CALcuLus

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  1. CALcuLus

  2. How do you know how fast You are going?

  3. “well how do you know How fast you’re going Right now, At this very second?”

  4. Push your friend so that his/her speed changes Try to measure their speed at any single point

  5. Paper darts Create your own paper dart. Which one is the ‘best’ design?

  6. Paper darts Model the flight path on a 2D co-ordinate plane. What are your variables? What is your graph telling us?

  7. Paper darts What is a tangent line? What are these lines telling us?

  8. Paper darts

  9. Fundamental theorem of CALcuLus

  10. Introduction to Calculus

  11. Calculus is a branch of mathematics that deals with finding and interpreting the gradients (slopes) of lines and curves

  12. The following graph shows f(x) = x + 1 or y = x + 1 (1, f(1)) To read the value of f(1), find 1 on the x-axis

  13. The following graph shows f(x) = −(x−2)4+3 or y = −(x−2)4+3 To read the value of x, where f(x) = 2; find 2 on the y axis (1, f(1)) and (3, f(3))

  14. A (4, f(4)) (1 ,f(1)) D Length AD = f(4) – f(1) = 5 – 2 = 3 units f(4) – f(1) is called the growth function as x changes from 1 to 4

  15. In calculus the points can be labelled (x, f(x)) and (x + h, f(x) + h)) f(x) (x + h, f(x + h)) (x, f(x)) x x + h x The growth function as x changes from x to x + h is given by f(x + h) – f(x)

  16. Find the growth of the function f(x) = 3x as ‘x’ changes from x to x + 4 Growth = f(x + 4) – f(x) = 3(x + 4) – 3x = 3x + 12 – 3x = 12

  17. Find the growth of the function f(x) = -6x +1 as ‘x’ changes from x to x + h Growth = f (x + h) – f(x) = (-6(x + h) + 1) – (-6x + 1) = -6x -6h + 1 + 6x -1 = -6h

  18. Sketching growth functions In your course book

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