Answer:
3
Step-by-step explanation:
Here we have the function
[tex]f(x)=3x-5[/tex]
We want to find the following ratio:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
Note that the limit of this for [tex]h\rightarrow 0[/tex] is equivalent to the derivative of the function.
Here we have:
[tex]f(x+h)=3(x+h)-5=3x+3h-5[/tex]
And
[tex]f(x)=3x-5[/tex]
Therefore we have
[tex]f(x+h)-f(x)=3x+3h-5-(3x-5)=3h[/tex]
And therefore,
[tex]\frac{f(x+h)-f(x)}{h}=\frac{3h}{h}=3[/tex]
