Answered

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
C1
D3

Verified Answer :

Panoyin

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

calculista

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 \(1\)


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