Estimate the slope of the tangent line (rate of change) to f(x)=1x\displaystyle {f{{\left({x}\right)}}}=\frac{{1}}{{x}} at x=1\displaystyle {x}={1} by finding the slopes of the secant lines through the points listed below.
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State answers to three decimal places

  1. (0.8,10.8)\displaystyle {\left({0.8},\frac{{1}}{{0.8}}\right)} and (1.2,11.2)\displaystyle {\left({1.2},\frac{{1}}{{1.2}}\right)}

    secant slope, msec⁡=\displaystyle {m}_{{{\sec}}}=

  2. (0.9,10.9)\displaystyle {\left({0.9},\frac{{1}}{{0.9}}\right)} and (1.1,11.1)\displaystyle {\left({1.1},\frac{{1}}{{1.1}}\right)}

    secant slope, msec⁡=\displaystyle {m}_{{{\sec}}}=

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