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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function `f(x)=(2x)/sqrt(x-1)` . The critical points of f(x) lie at the solution of f'(x) = 0.

f'(x) = `(2*sqrt(x - 1) - 2x*(1/2)*(1/sqrt(x - 1)))/(x - 1)`

=> `(2*sqrt(x - 1) - x*(1/sqrt(x - 1)))/(x - 1)`

=> `(2*(x - 1) - x)/((x - 1)*sqrt(x - 1))`

=> `(x - 2)/((x - 1)*sqrt(x - 1))`

f'(x) = 0

=> `(x - 2)/((x - 1)*sqrt(x - 1)) = 0`

=> x - 2 = 0

=> x = 2

The critical point of `f(x)=(2x)/sqrt(x-1)` is at x = 2.

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