From the rate of change given :
[tex]\frac{\triangle y}{\triangle x}=\text{ 2(2a + h)}[/tex]
The point given is represented (a, a+h), which is also (a, x)
For the point (2, 5), a = 2, x = 5
h = x - a = 5 - 2
h = 3
Substituting a = 2, and h = 3 into the above equation:
[tex]\begin{gathered} \frac{\triangle y}{\triangle x}=\text{ 2( 2}(2)\text{ + 3 )} \\ \frac{\triangle y}{\triangle x}=\text{ 2 (}4\text{ + 3)} \\ \frac{\triangle y}{\triangle x}=\text{ 2 (7)} \\ \frac{\triangle y}{\triangle x}=14 \end{gathered}[/tex]
For the point (5, 5), a = 5, x = 5
h = x - a
h = 5 - 5
h = 0
Substituting a = 5, and h = 0 into the equation:
[tex]\begin{gathered} \frac{\triangle y}{\triangle x}=\text{ 2(2a+h)} \\ \frac{\triangle y}{\triangle x}=\text{ 2 ( 2(5) + 0)} \\ \frac{\triangle y}{\triangle x}=\text{ 2 (10)} \\ \frac{\triangle y}{\triangle x}=\text{ 20} \end{gathered}[/tex]
