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