Math - Simple rational Function (check)

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Consider the function f(x) = x/(x-1)

Are there any turning points? Explain how this could help you graph f(x) for large values of x?

Ans: turning points is another word for checking the concavity, and therefore i find the second derivative and equate it to zero and see where it is concave up and down, using that information i can know when the graph is increasing or decreasing, with its end behaviors near the asymptote

  • Math - Simple rational Function (check) -

    Correct.
    Did you find any turning points?

  • Math - Simple rational Function (check) -

    I get the second derivative as f''(x) = 2/(x-1)^3. If f''(x) = 0 then there are no solutions, hence there are no turning points.

    Am i correct? But how does that help me graph f(x) for large values.

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