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11 Nov 2019
A differentiable function f has the properties(i) f(x) 0 for x > x0,(iii) f(7) = 7, f'(7) = 5.Use the tangent line at (7, 7) to the graph of f to compute an approximate value for the value of x0.
A differentiable function f has the properties(i) f(x) 0 for x > x0,(iii) f(7) = 7, f'(7) = 5.Use the tangent line at (7, 7) to the graph of f to compute an approximate value for the value of x0.
Keith LeannonLv2
25 Jan 2019
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| The figure shows how a function f(x) and its linear approximation (i.e., its tangent line) change value when x changes from x0 to x0+dx. Suppose f(x)=x2+4x, x0=2 and dx=0.04. Your answers below need to be very precise, so use many decimal places. (a) Find the change Îf=f(x0+dx)âf(x0)). Îf = (b) Find the estimate (i.e., the differential) df=fâ²(x0)dx. df = (c) Find the approximation error |Îfâdf| Error = |
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y= f(x) f(da) ETro Tangent df = f' (x)dx f(ro) T0
