The function f(x) has its fifth derivative continuous on (−∞,∞). (a) If |f(5)| < 6 on the interval [2.9,3.1], to how many decimal places does the fourth Taylor polynomial T4(x) of f(x) centered at 3 approximate f(x) on this interval? (b) If f(5) > 0 on the interval [2,4] find the values of x in this interval, if any, for which T4(x) over-approximates f(x) or under-approximates f(x).

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