# calculus

Find the critical numbers for the function
f(x) = 2x / sqrt(x-1)

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1. f(x) = 2x(x-1)^(-1/2)
f ' (x) = 2x(-1/2)(x-1)^(-3/2) + 2(x-1)^(-1/2)
= 0 for critical values, (max/mins)

x/(x-1)^(3/2) = 2/(x-1)^(1/2)
times (x-1)^(3/2)
x = 2(x-1)
x = 2x - 2
x = 2
f(2) = 4/sqrt(1) = 4

the critical number, in this case a minimum is (2,4)

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posted by Reiny

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