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How do I find f"(6)?

Estimate f″(0.6) by first estimating the first derivative at 0.4, 0.6, and 0.8.

Specifically, proceed as follows. Use the same technique that you used in part (1) to estimate f′(0.4). Next, use this same technique to estimate f′(0.8).

At this point, you will have computed the values of f′ at 0.4, 0.6, and 0.8. Reasoning in a similar manner to that used in part 1 above, use your estimates for f′(0.4), f′(0.6) and f′(0.8) to make an estimate for f″(0.6).

f'(6) was found to be 1.1

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  • You're not finding just f'(6) though, are you?

    f'(0.2) approximately (f(0.4) - f(0)) / (0.4 - 0)

    f'(0.4) app. (f(0.6 - f(0.2)) / (0.6 - 0.2)

    f'(0.6) app. (f(0.8) - f(0.4)) / (0.8 - 0.4)

    f'(0.8) app. (f(1) - f(0.6)) / (1 - 0.6)

    f'(1) app. (f(1.2) - f(1)) / (1.2 - 0.8)

    f'(0.2) = (11.44 - 1) / 0.4 = 10.44 / 0.4 = 52.2/2 = 26.1

    f'(0.4) = (11.66 - 11.22) / 0.4 = 0.44/0.4 = 1.1

    f'(0.6) = (11.88 - 11.44) / 0.4 = 0.44/0.4 = 1.1

    f'(0.8) = (17.1 - 11.66) / 0.4 = 5.44/0.4 = 27.2/2 = 13.6

    f'(1) = (17.32 - 17.1) / 0.4 = 0.22/0.4 = 22/40 = 0.55

    f''(0.6) = (f'(0.8) - f'(0.4)) / (0.8 - 0.4)

    f''(0.6) = (13.6 - 1.1) / 0.4 = 12.5/0.4 = 62.5/2 = 31.25

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