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Home > CALC > Chapter 2 > Lesson 2.4.1 > Problem 2-145

2-145.
  1. Given the function f(x) = 2x2x + 3, calculate the following values. Homework Help ✎

    1. Estimate

This is the slope of the secant between x = 3 and x = 2, otherwise known as Average Rate of Change (AROC).

This is the slope of the secant between x = 2.1 and x = 2.

And this is the slope of the secant between x =____ and x =____.

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 x = 2. 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?