Question

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Find all critical numbers and use the Second Derivative Test to determine all local extrema. f(x) = x2-1/x f'(x) = (x)(2x)-(1)(x2 - 1)/x2 = 2x2 - x2 + 1/x2 = x2 + 1/x2 = > f'(x) = x2 = 0 = >x = 0 = > f'(x) = x2 + l = 0 = > x -1 When the denominator = 0 the function is undefined and when setting the numerator to zero it is impossible to set it equal to zero (square root of a negative number). f'(x) = x2 + 1/x2 f"(x) = (x2)(2x)-(x2 + 1)(2x)/(x2)2 = 2x3 - 2x3 - 2x/x4 = -2x/x4 f"(0) = -2(0)/(0)4 = undefined This graph has no local extrema.

Show transcribed image text Find all critical numbers and use the Second Derivative Test to determine all local extrema. f(x) = x2-1/x f'(x) = (x)(2x)-(1)(x2 - 1)/x2 = 2x2 - x2 + 1/x2 = x2 + 1/x2 = > f'(x) = x2 = 0 = >x = 0 = > f'(x) = x2 + l = 0 = > x -1 When the denominator = 0 the function is undefined and when setting the numerator to zero it is impossible to set it equal to zero (square root of a negative number). f'(x) = x2 + 1/x2 f"(x) = (x2)(2x)-(x2 + 1)(2x)/(x2)2 = 2x3 - 2x3 - 2x/x4 = -2x/x4 f"(0) = -2(0)/(0)4 = undefined This graph has no local extrema.