easy

no. of distinct real roots of f"(x) if f(x)=(x-1)²⁵(x-2)⁴³(x-3)¹¹

2 Answers

Let \; f'(x)=k(x)f(x) \; then f"(x)=f(x)[k^{2}(x)+k'(x)]

k(x)=\frac{25}{(x-1)}+\frac{43}{(x-2)}+\frac{11}{(x-3)}

341

Hari Shankar ·2010-03-15 18:20:02

That reasoning fails with repeated roots. x=1,2,3 are roots of f"(x) = 0 too

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