Doug C. answered • 29d

Math Tutor with Reputation to make difficult concepts understandable

Consider asking yourself the question "for what value of x does 1+5x = 11.005"?

Realize that f(2) = [1 + 5(2)]^{1/7} or (11)^{1/7}.

And f(2.001) = [1+ 5(2.001)]^{1/7} = 11.005^{1/7}

So, if your linearization is L(x) = .0914x + 1.22 (you might not have rounded off quite correctly there), then L(2.001) should give a fair approximation for f(11.005).