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Consider the function f(x) = x^2/x-1 with f ' (x) = x^2-2x/ (x - 1)^2 and...

Consider the function f(x) = x^2/x-1 with f ' (x) = x^2-2x/ (x - 1)^2 and f '' (x) = 2 / (x - 1)^3 are given. Use these to answer the following questions.

(a) [5 marks] Find all critical points and determine the intervals where f(x) is increasing and where it is decreasing, use the First Derivative Test to fifind local extreme value if any exists.

(b) Determine the intervals where f(x) is concave upward and where it is concave downward. Use the Second Derivative Test to verify local extreme values from part (a).

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