Estimate the slope of the tangent line (rate of change) to f(x)=x2\displaystyle {f{{\left({x}\right)}}}={x}^{{2}} at x=−1\displaystyle {x}=-{1} by finding the slopes of the secant lines through the points:

  1. (−2,4)\displaystyle {\left(-{2},{4}\right)} and (0,0)\displaystyle {\left({0},{0}\right)}

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

  2. (−1.5,2.25)\displaystyle {\left(-{1.5},{2.25}\right)} and (−0.5,0.25)\displaystyle {\left(-{0.5},{0.25}\right)}

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

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