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Differentiation; Revision Overview

Differentiation; Revision Overview. Differentiation. Given Y = ax n then differentiating . Rule Multiply by the power and take one off. Differentiation. You can be asked to write down the first and second differentials in an A/S question. Remember

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Differentiation; Revision Overview

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  1. Differentiation; Revision Overview

  2. Differentiation Given Y = axn then differentiating Rule Multiply by the power and take one off

  3. Differentiation You can be asked to write down the first and second differentials in an A/S question. Remember y = gives information about the (x,y) curve gives information about the gradient of the tangent to the curve gives information about the nature of the stationary point(s) on the curve

  4. Differentiation Basic differentiation by Rule Q

  5. Differentiation: Basic rule Answer

  6. Differentiation You can be asked to find the value of the gradient of the tangent at a given (a) point x on the curve or (b) co-ordinate point on the curve Method Step 1 differentiate to find Step 2 calculate the value of at the calculated x value

  7. Differentiation gradient at a point Answer

  8. Differentiation gradient at a point Answer

  9. Differentiation To find the gradient write down the x coordinate i.e x = 4

  10. Differentiation

  11. Differentiation Stationary point on a quadratic curve Step 1 Differentiate and set Step 2 Solve the resulting linear equation for x Step 3 Substitute back into the curve equation to find the y co-ordinate. Step 4 Determine the nature of the turning point. Write down interpret its sign. positive implies minimum negative implies maximum

  12. Differentiation: Stationary Point Question The curve has an equation y = 1 + 4x – x2 Calculate the coordinates of the point labelled A on the curve shown in the diagram. y A x

  13. y A x Differentiation: Stationary Point answer Answer The curve has an equation y = 1 + 4x – x2 Differentiate Point A is a turning point i.e Y = 1 + 4(2) – (2)2 = 5 Coordinates of A (2, 5) (2, 4 ) Nature of turning point Negative Maximum

  14. Differentiation Stationary point on a cubic curve Step 1 Differentiate and set Step 2 Solve the resulting quadratic equation for x Step 3 Substitute back into the curve equation to find the corresponding y co-ordinates. Step 4 Determine the nature of the turning points. Using the test.

  15. Differentiation Test for the nature of the turning points Step 1 Differentiate to obtain Step 2 Substitute each x value into Step 3 If then curve takes a Minimum If then curve takes a Maximum At the two turning points

  16. Differentiation Stationary Points on a curve Q

  17. Differentiation Answer

  18. Differentiation points turning Answer Answer continued

  19. Differentiation Turning point Answer Graph with turning points clearly labelled. y = x3- 6x2 -15x + 1

  20. Differentiation: Stationary Points on a curve. B Question The curve has an equation y = 5 + 3x2 – x3 Calculate the coordinates of the points labelled A and B on the curve shown in the diagram. y B y x A

  21. Differentiation stationary points Answer Answer

  22. Differentiation stationary points Answer Answer

  23. Differentiation: Stationary Points on a curve. Answer Answer The curve has an equation y = 5 + 3x2 – x3 the coordinates of the points labelled A and B are: A(0,5) and B(2,9) Max B y y B(2,9) x x A(0,5) A Min

  24. Differentiation: Stationary points on a curve. Question Calculate the coordinates of the stationary points on the curve y = x3 - 3x + 2 Determine the nature of each of the stationary points.

  25. Differentiation stationary points Answer Answer

  26. Differentiation stationary points Answer Answer

  27. Differentiation: Stationary Points on a curve. Answer Answer The curve has an equation y = x3- 3x + 2 the coordinates of the turning points labelled (-1, 4) and (1, 0) y (-1,4) Max x (1,0) Min

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