### Home > CALC > Chapter Ch2 > Lesson 2.4.1 > Problem 2-145

2-145.

Given the function

*f*(*x*) = 2*x*^{2}−*x*+ 3, calculate the following values. Homework Help ✎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?