ConcepTest Section 3.9 Question 1 In which of the following graphs will using local linearity to approximate the value of the function near x = c give.

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Presentation transcript:

ConcepTest Section 3.9 Question 1 In which of the following graphs will using local linearity to approximate the value of the function near x = c give the least error as ∆x becomes larger?

ConcepTest Section 3.9 Answer 1 ANSWER (d). Local linearity will give exact answers in graph (d) because the tangent line at x = c is identical with the graph on the interval shown. COMMENT: You could lay a pencil on the overhead to illustrate the tangent line in each case.

ConcepTest Section 3.9 Question 2 To estimate the numerical value of the square root of a number, we use a tangent line approximation about x = a. From Figure 3.14, the graph of decide for which number the error in using this approximation has the smallest magnitude.

ConcepTest Section 3.9 Answer 2 ANSWER (e). The least error occurs at the point closest to the perfect square whose tangent line has the flattest slope. Thus the answer is (e). COMMENT: You could ask the students why the approximation is taken about perfect squares. You could also have students graph on the window 0 < x < 17, 0 < y < 4.5 and have their graphing calculator draw tangent lines at the appropriate points.