for the function f(x) = 5x + 6, evaluate and simplify the difference quotient.
for the function f(x) = 5x + 6, evaluate and simplify the difference quotient.
Answer
Explanation:
Step1: Recall the difference - quotient formula
The difference - quotient for a function $y = f(x)$ is $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$. Given $f(x)=5x + 6$, first find $f(x + h)$. $f(x + h)=5(x + h)+6=5x+5h + 6$.
Step2: Substitute $f(x + h)$ and $f(x)$ into the difference - quotient formula
$\frac{f(x + h)-f(x)}{h}=\frac{(5x + 5h+6)-(5x + 6)}{h}$.
Step3: Simplify the numerator
$(5x + 5h+6)-(5x + 6)=5x+5h + 6 - 5x - 6=5h$.
Step4: Simplify the fraction
$\frac{5h}{h}=5$.
Answer:
$5$