MATH 102 Lecture 11: Linear Approximation overestimation or underestimation, Newton’s Method
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Lecture 11 - linear approximation overestimation or underestimation, newton"s method. , using linear approximation to determine f(8. 75), and if the result is an overestimate or an underestimate. Step 1: use a nice value you know to be x0, such as 9, because. Step 2: according to the linear approximation"s function f(x) , nd all individual values of f(x0) and f"(x0) f(x0)+f"(x0)(x-x0) Step 4: check if it is an overestimate or an underestimate by drawing the function on a graph. When x near 0, smaller power dominates, so function becomes # f (x) = When x >> 0, lager power dominates, so function becomes # f (x) = Using these information, the graph would look like. So when f(8. 75), the tangent line would be above the function, so. = xk f (xk ) f "(xk : it is used for a more accurate approximation.
