Question

given that f(x)=5x² + 8x - 13, determine an expression in terms of x and h that represents the average rate of change of f over any interval of length h. that is, over any interval (x,x + h). in words, find the difference quotient for f(x). simplify your answer as much as possible. 10x+5h+8 preview submit question 8. points possible: 2 unlimited attempts. score on last attempt: 2. score in gradebook: 2 message instructor about this question post this question to forum given the constant function f(x)=84, determine an expression in terms of x and h that represents the average rate of change of f over any interval of length h. that is, over any interval (x,x + h). in other words, find the difference quotient for f(x). simplify your answer as much as possible. (hint: graph f(x)=84. what does that graph look like?) enter an algebraic expression more... preview submit question 9. points possible: 2 unlimited attempts. message instructor about this question post this question to forum given that f(x)=11x + 4.5, determine an expression in terms of x and h that represents the average rate of change of f over any interval of length h. that is, over any interval (x,x + h). in other words, find the difference quotient for f(x). simplify your answer as much as possible.

Explanation:

Step1: Recall difference - quotient formula

The difference - quotient for a function $y = f(x)$ over the interval $(x,x + h)$ is $\frac{f(x + h)-f(x)}{h}$.

Step2: For $f(x)=84$

First, find $f(x + h)$. Since $f(x)=84$ is a constant function, $f(x + h)=84$.
Then, substitute into the difference - quotient formula: $\frac{f(x + h)-f(x)}{h}=\frac{84 - 84}{h}$.

Step3: Simplify the expression

$\frac{84 - 84}{h}=\frac{0}{h}=0$.

Step1: Recall difference - quotient formula

The difference - quotient for a function $y = f(x)$ over the interval $(x,x + h)$ is $\frac{f(x + h)-f(x)}{h}$.

Step2: For $f(x)=11x + 4.5$

Find $f(x + h)$: $f(x + h)=11(x + h)+4.5=11x+11h + 4.5$.
Then, substitute into the difference - quotient formula: $\frac{f(x + h)-f(x)}{h}=\frac{(11x+11h + 4.5)-(11x + 4.5)}{h}$.

Step3: Simplify the expression

$\frac{11x+11h + 4.5-11x - 4.5}{h}=\frac{11h}{h}=11$.

Answer:

$0$