Question

Use the following table of the function f(x) = x4 − 4x to answer this question:

Answer 1

$A(x) = \frac{f(x) - f(a)}{x - a} = \frac{f(-1) - f(2)}{-1 - 2} = \frac{5 - 8}{-3} = \frac{-3}{-3} = 1$
The answer is C.

Answer 2

we have

$f(x)=x^{4}-4x$

Step 1

Using the table find the value of f(x) for $x=-1$

$x=-1\\f(-1)=5$

Step 2

Using the table find the value of f(x) for $x=2$

$x=2\\f(2)=8$

Step 3

Find the average rate of change

we know that

the average rate of change is equal to the formula

$\frac{f(b)-f(a)}{b-a}$

in this problem we have

$f(b)=f(2)=8$

$f(a)=f(-1)=5$

$b=2$

$a=-1$

substitute the values in the formula

$\frac{8-5}{2+1}$

$\frac{3}{3}=1$

therefore

the answer is the option C

the average rate of change is $1$