Find the average rate of change of the function from x₁ = 1 to x₂ = 5.? $$f ( x ) = x ^ { 2 } + 18 x - 4$$ ? A)The average rate of change from x₁ = 1 to x₂ = 5 is 24. B)The average rate of change from x₁ = 1 to x₂ = 5 is -4. C)The average rate of change from x₁ = 1 to x₂ = 5 is -24. D)The average rate of change from x₁ = 1 to x₂ = 5 is -18. E)The average rate of change from x₁ = 1 to x₂ = 5 is 4.

Question

Quizplus · Accepted Answer

The average rate of change of a function $f(x)$ over the interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. For $f(x) = x^2 + 18x - 4$, from $x = 1$ to $x = 5$, we calculate $f(5) = 5^2 + 18(5) - 4 = 25 + 90 - 4 = 111$ and $f(1) = 1^2 + 18(1) - 4 = 15$. Thus, the average rate of change is $\frac{111 - 15}{5 - 1} = \frac{96}{4} = 24$.

Find the Average Rate of Change of the Function from X1

Find the Average Rate of Change of the Function from X₁