The figure shows how a function $f(x)$ and its linear approximation (i.e., its tangent line) change value when $x$ changes from $x_0$ to $x_0 + dx$. Suppose $f(x) = x^{2}-4x$, $x_0 = 1$ and $dx = 0.04$. Your answers below need to be very precise, so use many decimal places. (a) Find the change $\Delta f = f(x_0+dx)-f(x_0)$. $\Delta f$ = (b) Find the estimate (i.e., the differential) $df = f'(x_0) \, dx$. $df$ = (c) Find the approximation error $|\,\Delta f - df \, |$. Error =

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You can earn partial credit on this problem.