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    First Principle in evaluating derivatives

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    (A) Find and simplify the difference quotient for G(X)=1/x^2. HINT: After finding the difference quotient, simplify by using an LCD to combine the fractions.

    (B) Using the answer above, find the value of the difference quotient at x=1 with an h=.1

    C) Sketch a graph of G(x). Mark the point(1,G(1)) on the graph. Sketch a tiny line segment at this point which is tangent to the graph of G(x).

    D) Considering the value of the difference quotient at x=1, is G(x) increasing or decreasing at this point?
    What does the absolute value of the difference quotient tell you about G(x) at this point?
    Write a few sentences of explanation of your understanding of this concept.

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    Solution Summary

    The solution discusses the first principle in evaluating derivatives in the given problem.