Let f(x) = 3+7x Compute f(x) f'(2) = f (z) = f(1) f'(1) f(1)= f(x) =...

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Let f(x) = 3+7x Compute f(x) f'(2) = f" (z) = f(1) f'(1) f"(1)= f""(x) = f""(1) = f(iv)(x)= f(i)(1)= f()(x) = f()(1)= We see that the first term does not fit a pattern, but we also see that f()(1) = Hence we see that the Taylor series for centered at 1 is given by f(x)=10+(x-1)* k-1 for k1. Let f(x) = 3+7x Compute f(x) f'(2) = f" (z) = f(1) f'(1) f"(1)= f""(x) = f""(1) = f(iv)(x)= f(i)(1)= f()(x) = f()(1)= We see that the first term does not fit a pattern, but we also see that f()(1) = Hence we see that the Taylor series for centered at 1 is given by f(x)=10+(x-1)* k-1 for k1.