find the average rate of change of the function $f(x) = x^2 + 7x$ from $x_1 = 4$ to $x_2 = 5$.

the average rate of change is (simplify your answer.)

Question

find the average rate of change of the function $f(x) = x^2 + 7x$ from $x_1 = 4$ to $x_2 = 5$.

the average rate of change is   (simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change" ] } ## State the average rate of change formula Using the *Average Rate of Change* knowledge point $$ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} $$ ## Evaluate the function at the given endpoints Using the *Average Rate of Change* knowledge point $$ \begin{aligned} f(4) &= (4)^2 + 7(4) = 16 + 28 = 44 \ f(5) &= (5)^2 + 7(5) = 25 + 35 = 60 \end{aligned} $$ ## Calculate the average rate of change Using the *Average Rate of Change* knowledge point $$ \frac{f(5) - f(4)}{5 - 4} = \frac{60 - 44}{5 - 4} = \frac{16}{1} = 16 $$ Find the average rate of change of the function $f(x) = x^2 + 7x$ from $x_1 = 4$ to $x_2 = 5$. The average rate of change is 16 (Simplify your answer.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

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Explanation:

State the average rate of change formula

Evaluate the function at the given endpoints

Calculate the average rate of change

Answer: