Question

They want me to find the rate of change for 5. I already did it for 2.

Answer 1

From the rate of change given :

`(\triangle y)/(\triangle x)=\text{ 2(2a + h)}`

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:

`\begin{gathered} (\triangle y)/(\triangle x)=\text{ 2( 2}(2)\text{ + 3 )} \\ (\triangle y)/(\triangle x)=\text{ 2 (}4\text{ + 3)} \\ (\triangle y)/(\triangle x)=\text{ 2 (7)} \\ (\triangle y)/(\triangle x)=14 \end{gathered}`

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:

`\begin{gathered} (\triangle y)/(\triangle x)=\text{ 2(2a+h)} \\ (\triangle y)/(\triangle x)=\text{ 2 ( 2(5) + 0)} \\ (\triangle y)/(\triangle x)=\text{ 2 (10)} \\ (\triangle y)/(\triangle x)=\text{ 20} \end{gathered}`