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f(x) and its linear approximation (i.e., its tangent line) change value when a changes from to xo + dx. Suppose f(x) = x² + 6x, * = 3 and dx = 0.05. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f(xo + dx) - f(xo). Af = f(xo+da) f(xo) Af = f(xo+da)-f(x) 20 da Error = |Af-df| |df = f'(x)da ro+dr (Click on graph to enlarge) Tangent

f(x) and its linear approximation (i.e., its tangent line) change value when a changes from to xo + dx. Suppose f(x) = x² + 6x, * = 3 and dx = 0.05. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f(xo + dx) - f(xo). Af = f(xo+da) f(xo) Af = f(xo+da)-f(x) 20 da Error = |Af-df| |df = f'(x)da ro+dr (Click on graph to enlarge) Tangent

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 7CR
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The figure shows how a function f(x) and its linear approximation (i.e., its tangent line) change value when a changes from to to + dx. Suppose f(x) = x² + 6x, *₁ = 3 and dx = 0.05. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f(xo + dx) - f(xo). Af = 0 (b) Find the estimate (i.e., the differential) df = f'(x) dx. df = (c) Find the approximation error | Af-df. Error = f(xo + dr) f(xo) |Af = f(xo+dx)-f(ao) 20 dx y = f(x) (Click on graph to enlarge) Error = |Af-df| to + dr Tangent df = f'(x)da
Transcribed Image Text:The figure shows how a function f(x) and its linear approximation (i.e., its tangent line) change value when a changes from to to + dx. Suppose f(x) = x² + 6x, *₁ = 3 and dx = 0.05. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f(xo + dx) - f(xo). Af = 0 (b) Find the estimate (i.e., the differential) df = f'(x) dx. df = (c) Find the approximation error | Af-df. Error = f(xo + dr) f(xo) |Af = f(xo+dx)-f(ao) 20 dx y = f(x) (Click on graph to enlarge) Error = |Af-df| to + dr Tangent df = f'(x)da
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