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Home > PCT > Chapter Ch8 > Lesson 8.2.4 > Problem 8-126

8-126.

Given the function $f(x)=10-x^2$ , find the slope of the line between the following pairs of points.

$(2,f(2))$ and $(4,f(4))$
Step (a):
$m=\frac{f(4)-f(2)}{4-2}$

$(2,f(2))$ and $(3,f(3))$
Step (b):
$m=\frac{f(3)-f(2)}{3-2}$

$(2,f(2))$ and $(2.5,f(2.5))$
Step (c):
$m=\frac{f(2.5)-f(2)}{2.5-2}$

$(2,f(2))$ and $(2.1,f(2.1))$
Step (d):
$m=\frac{f(2.1)-f(2)}{2.1-2}$

As the two points get closer and closer, what happens to the slope of the line?

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