The average rate of change of f(x) = −2x + 1 from x = −5 to x = 1 is "2".
Step-by-step explanation:
We have to find the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1
The formula to calculate the average rate of change of function f(x) from point a to point b can be calculated as:
Average rate of change = [tex]\frac{f(b) - f(a)}{b - a}[/tex]
In this question
a = -5
b = 1
f(a) = f(-5) = -2(-5) + 1
f(-5) = 10 + 1
f(-5) = 11
f(b) = f(1) = -2(1) + 1
f(1) = -2 + 1
f(1) = -1
Putting these values in the formula, we get
Average rate of change = [tex]\frac{f(-5) - f(1)}{ 1 - (-5)}[/tex]
Average rate of change = [tex]\frac{f(-5) - f(1)}{ 1 - (-5)}[/tex]
Average rate of change = [tex]\frac{11 - (-1)}{ 1 + 5)}[/tex]
Average rate of change = [tex]\frac{11 +1 }{ 6 }[/tex]
Average rate of change = [tex]\frac{12}{ 6}[/tex]
Average rate of change = 2
Therefore, the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1 is "2".
Keywords: rate of change
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