MATH 115 Chapter Notes - Chapter 2: Linearization, Mean Value Theorem
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3. 9 linear approximation (computing the tangent line) skipping 3. 8, won(cid:495)t be tested. And we know that this line is the tangent line at our point. Key point is that the graph of f looks like a straight line, tangent line. In other words, close to out point (a) f looks like a tangent line at (a). Slope of the tangent line is derivative: equation for tangent line using this formula, call the equation for the tangent line the local linearization of f at (a) or the tangent line approximation at (a). If e(x) is greater than zero, the tangent line approximation is an underestimate. If e(x) is less than zero, the tangent line approximation is an overestimate. The tangent line approximation is an underestimate when f(x) is concave up: (graph on top, tangent line on bottom) The tangent line approximation is an overestimate when f(x) is concave down: (tangent line on top, graph on bottom)
