For a given function f(x), we define the difference quotient as:
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
We will get that the difference quotient is equal to 6.
Here we have the function:
f(x) = 6*x + 1
The difference quotient will be:
[tex]\frac{f(x + h) - f(x)}{h} = \frac{6*(x + h) + 1 - (6*x + 1)}{h}[/tex]
Now let's simplify it:
[tex]\frac{6*(x + h) + 1 - (6*x + 1)}{h} = \frac{6*x + 6*h + 1 - 6*x - 1}{h} = \frac{6*h}{h} = 6[/tex]
Now, we also are asked to evaluate it, but as you can see, the difference quotient is constant, thus we can't actually evaluate it, as it will always be equal to 6.
If you want to learn more, you can read:
https://brainly.com/question/18270597
