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Discuss the properties of the linear function

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Reference no: EM131613760

Question: A function f(x, y, z) has the property that f(1, 0, 1) = 20, f(1, 1, 1) = 16, and f(1, 1, 2) = 21.

(a) Estimate f(1, 1, 3) and f(1, 2, 1), assuming f is a linear function of each variable with the other variables held fixed.

(b) Suppose in fact that f(x, y, z) = ax2 + byz + czx3 + d2x - y, for constants a, b, c and d. Which of your estimates in part (a) do you expect to be exact?

(c) Suppose in addition that f(0, 0, 1) = 6. Find an exact formula for f by solving for a, b, c, and d.

(d) Use the formula in part (c) to evaluate f(1, 1, 3) and f(1, 2, 1) exactly. Do the values confirm your answer to part (b)?

Reference no: EM131613760

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