Question

(1 point)

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 Δf=f(x0+dx)−f(x0)). Δf = (b) Find the estimate (i.e., the differential) df=f′(x0)dx. df = (c) Find the approximation error |Δf−df| Error =

(Click on graph to enlarge)

y= f(x) f(da) ETro Tangent df = f' (x)dx f(ro) T0