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2. (105L worksheet: Linear Approximations) Find the linear approximation to the func tion f(ac) 2 cock: at a: = 0. Assuming that k > 0,
2. (105L worksheet: Linear Approximations) Find the linear approximation to the func tion f(ac) 2 cock\": at a: = 0. Assuming that k > 0, does the linear approximation overestimate or underestimate we\" near 0? Explain your answer carefully. 3. (105L worksheets: The Derivative Function, The Second Derivative, and Using First and Second Derivatives) On the axes to the right, identify which 3/ graph represents f (m), which represents f'(a:) and which represents f"(2:). Briey explain your reasoning. 4. (105L Linear modeling lab, Chain Rule Worksheet) Using the table below, estimate 6%. (g(a:)) at at = 1.3 as closely as possible. Explain your reasoning. (Hint: You will need the chain rule, but you will also need to estimate derivatives. What is the ideal way to estimate them from data?) m 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 f(ac) 1.4 1.2 1.1 1.0 1.3 1.4 1.7 1.5 1.6 2.1 2.2 9(1') 0.9 1.4 2.2 2.0 1.9 1.5 2.2 3.1 2.5 2.2 2.3
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