Answer:
Difference quotient: [tex]\frac{f(x+h)-f(x)}{h}[/tex] = 2
Step-by-step explanation:
The difference quotient is the word that we use when trying to calculate the average rate of change of the function over a specific interval, which in this case, is h.
The formula for calculating the difference quotient is:
- [tex]\frac{f(x+h)-f(x)}{h}[/tex]
In order to determine the difference quotient of the function [tex]f(x)=2x-5[/tex] we need to first evaluate [tex]f(x+h)[/tex] of this function.
We can do so by substituting x + h for x into the function.
- [tex]f(x+h)=2(x+h)-5[/tex]
Distribute 2 inside the parentheses.
- [tex]f(x+h)=2x+2h-5[/tex]
Now that we have found f(x + h), we can use the formula for the difference quotient and substitute f(x + h) and f(x) into it:
- [tex]\frac{(2x+2h-5)-(2x-5)}{h}[/tex]
Distribute the negative sign inside the parentheses.
- [tex]\frac{2x+2h-5-2x+5}{h}[/tex]
Combine like terms in the numerator. The 2x and 5's cancel out. We are left with:
The h's cancel out, and this simplifies to:
The difference quotient of f(x) is 2.
