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Question: the derivative of 1 1 05 2...

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The derivative of 𝑓(𝑥) = 1 (1 − 0.5𝑥 2 ⁄ ) is 𝑓 ′ (𝑥) = 𝑥 (1 − 0.5𝑥 2 ) 2 ⁄ . Do you expect to have difficulties evaluating 𝑓 ′ (𝑥) at x = 1.41 (three digit precision square root of two)? Try it using 3- and 4-digit chopping. Note that 3/7 = 0.42857143 rounded to eight significant digits, but is 0.4285 with 4-digit chopping. Also, use only the *, /, +, and – keys and chop after each operation. This means that 𝑥 3 involves chopping after x*x and again after multiplying that result by x. This kind of chopping is the decimal equivalent to computer round off of floating point numbers.

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