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2-145.

Given the function , calculate the following values.

  1. This is the slope of the secant between and , otherwise known as Average Rate of Change (AROC).

  1. This is the slope of the secant between and .

  1. And this is the slope of the secant between ____ and ____.

  1. Estimate .

    Notice that as you progressed through parts (a), (b) and (c), the secant line becomes smaller and smaller, squeezing in on the actual slope at . Based on the patterns you see as the secant line decreases, what do you think the slope of the smallest possible secant line will be?