Mathematics

Mathematics

Problem

For p(x)=x4−8x2+7p(x)=x^{4}-8x^{2}+7, which of the following statements about its relative extrema is true? a) pp has relative maxima of equal value at x=−2x=-2 and x=2x=2, and a relative minimum at x=0x=0. b) pp has relative minima of equal value at x=−2x=-2 and x=2x=2, and a relative maximum at x=0x=0. c) pp has relative minima at x=−2x=-2 and x=2x=2 but no relative maximum, because the derivative does not change sign at x=0x=0. d) pp has relative minima of equal value at x=−2x=-2 and x=0x=0, and a relative maximum at x=2x=2.

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