Question
Find the average rate of change of the function \( f(x)=8 x \) from \( x_{1}=0 \) to \( x_{2}=6 \). The average rate of change is \( \square \). (Simplify your answer.)
Ask by Mcfarlane Vargas. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The average rate of change is 8.
Solution
The average rate of change of a function f(x) from x₁ to x₂ is given by the formula:
[f(x₂) − f(x₁)] / (x₂ − x₁).
For the function f(x) = 8x, with x₁ = 0 and x₂ = 6:
f(6) = 8(6) = 48
f(0) = 8(0) = 0
Substitute these values into the formula:
(48 − 0) / (6 − 0) = 48 / 6 = 8
Thus, the average rate of change is 8.
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Simplify this solution Mind Expander
To find the average rate of change of the function \( f(x) = 8x \) from \( x_1 = 0 \) to \( x_2 = 6 \), we can use the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] Calculating \( f(0) \) and \( f(6) \): \[ f(0) = 8(0) = 0 \] \[ f(6) = 8(6) = 48 \] Now using the average rate of change formula: \[ \text{Average Rate of Change} = \frac{48 - 0}{6 - 0} = \frac{48}{6} = 8 \] Thus, the average rate of change is \( 8 \).
