what is the average rate of change for the function $f(x) = \sqrt3{x - 3}$, to the nearest hundredth over the interval $-3 \le x \le 1$?

average rate of change:

Question

what is the average rate of change for the function $f(x) = \sqrt3{x - 3}$, to the nearest hundredth over the interval $-3 \le x \le 1$?

average rate of change:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Cube Root Functions" ] } ## Evaluate the function at the interval endpoints $$ \begin{aligned} f(-3) &= \sqrt[3]{-3 - 3} = \sqrt[3]{-6} \approx -1.81712\ f(1) &= \sqrt[3]{1 - 3} = \sqrt[3]{-2} \approx -1.25992 \end{aligned} $$ ## Calculate the average rate of change $$ \begin{aligned} \text{Average Rate of Change} &= \frac{f(1) - f(-3)}{1 - (-3)}\ &= \frac{\sqrt[3]{-2} - \sqrt[3]{-6}}{4}\ &\approx \frac{-1.25992 - (-1.81712)}{4}\ &= \frac{0.55720}{4}\ &\approx 0.1393 \end{aligned} $$ ## Round to the nearest hundredth $$ 0.1393 \approx 0.14 $$ What is the average rate of change for the function $f(x) = \sqrt[3]{x - 3}$, to the nearest hundredth over the interval $-3 \le x \le 1$? average rate of change: 0.14 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

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Question

Explanation:

Evaluate the function at the interval endpoints

Calculate the average rate of change

Round to the nearest hundredth

Answer: