contestada

Use the following table of the function f(x) = x4 − 4x to answer this question:
x f(x)
-2 24
-1 5
0 0
1 -3
2 8
What is the average rate of change from x = −1 to x = 2?
A. −3
B. −1
C. 1
D. 3

Respuesta :

Panoyin
[tex]A(x) = \frac{f(x) - f(a)}{x - a} = \frac{f(-1) - f(2)}{-1 - 2} = \frac{5 - 8}{-3} = \frac{-3}{-3} = 1[/tex]
The answer is C.
calculista

we have

[tex]f(x)=x^{4}-4x[/tex]

Step 1

Using the table find the value of f(x) for [tex]x=-1[/tex]

[tex]x=-1\\f(-1)=5[/tex]

Step 2

Using the table find the value of f(x) for [tex]x=2[/tex]

[tex]x=2\\f(2)=8[/tex]

Step 3

Find the average rate of change

we know that

the average rate of change is equal to the formula

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

in this problem we have

[tex]f(b)=f(2)=8[/tex]

[tex]f(a)=f(-1)=5[/tex]

[tex]b=2[/tex]

[tex]a=-1[/tex]

substitute the values in the formula

[tex]\frac{8-5}{2+1}[/tex]

[tex]\frac{3}{3}=1[/tex]

therefore

the answer is the option C

the average rate of change is [tex]1[/tex]


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