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substitute into the formula:

Now and we have

The difference quotient is 13. It is also the slope of the line from

b) We substitute and into the formula:

Now and and we have

c) We substitute and into the formula:

Now and and we have

Note the trend in the average rate of change as h gets closer to 0.

f15.012 - f152

0.01

=

25.1001 - 25

0.01

=

0.1001

0.01

= 10.01.

f15.012 = 15.0122 = 25.1001 f152 = 25,

f1x + h2 - f1x2

h

=

f15 + 0.012 - f152

0.01

=

f15.012 - f152

0.01

.

x = 5 h = 0.01

f15.12 - f152

0.1

=

26.01 - 25

0.1

=

1.01

0.1

= 10.1.

f15.12 = 15.122 = 26.01 f152 = 25,

f1x + h2 - f1x2

h

=

f15 + 0.12 - f152

0.1

=

f15.12 - f152

0.1

.

x = 5 h = 0.1

15, 252 to 18, 642.

f182 - f152

3

=

64 - 25

3

=

39

3

= 13.