Question: differentiation question 6. Sabah is using a spreadsheet to investigate the gradient of the curve y = x* .She uses the spreadsheet to calculate the

differentiation question

6. Sabah is using a spreadsheet to investigate the gradient of the curve y = x* .She uses the spreadsheet to calculate the gradient of the chord from the point where x = 2 to the point where x = 2+ h for different values of h. Part of her spreadsheet is shown below. A B C D E F 1 X f(x) h xth f (xth) Gradient 2 2 16 1 3 81 65 3 2 16 0.1 2.1 34.481 4 2 16 0.01 2.01 16.32240801 5 2 16 0.001 16.03202401 32.024008 6 2 16 0.0001 2.0001 16.00320024 32.00240008 (a) Fill in the missing values in cells D5, E3 and F4. [4] (b) Use differentiation from first principles to show that the gradient of the curve y = x" at the point where x = 2is 32. [3]

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