Find approximate value of $f (x) = x^{3} - 3 x + 5$ at $x = 1.99$

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Solution

$f (x) = x^{3} - 3 x + 5$ at $x = 1.994$
$f (1.994) = (1.994)^{3} - 3 (1994) + 5$
$= (2 - 0.006)^{3} - 3 (2 - 0.006) + 5$
$= 2^{3} - (0.006)^{3} - 3 (2) (0.006) [2 - 0.006] - 6 + 3 \times 0.006 + 5$
$f (1.994) = 6.9462$

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