Mathematics

Mathematics

Problem

Let h(x)=x3−6x2+11x−6h(x)=x^{3}-6x^{2}+11x-6, which has simple zeros at x=1,2,3x=1,2,3. A student wants to approximate the zero at x=2x=2 using interval halving on an interval of length 0.80.8. Which interval choice both contains exactly one zero and is such that hh is strictly monotonic throughout the interval? a) [1.8,2.6][1.8,2.6] b) [1.5,2.3][1.5,2.3] c) [2.2,3.0][2.2,3.0] d) [1.5,2.2][1.5,2.2]

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