given $f(x) = 17 - x^2$, what is the average rate of change in $f(x)$ over the interval $1, 5$?

$\bigcirc$ $-6$
$\bigcirc$ $-\frac{1}{2}$
$\bigcirc$ $\frac{1}{4}$
$\bigcirc$ $1$

Question

given $f(x) = 17 - x^2$, what is the average rate of change in $f(x)$ over the interval $1, 5$?

$\bigcirc$ $-6$
$\bigcirc$ $-\frac{1}{2}$
$\bigcirc$ $\frac{1}{4}$
$\bigcirc$ $1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change on Interval" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change on Interval", "Function Evaluation" ] } ## Evaluate the function at the interval endpoints $$ \begin{aligned} f(1) &= 17 - (1)^2 = 16 \ f(5) &= 17 - (5)^2 = 17 - 25 = -8 \end{aligned} $$ ## Calculate the average rate of change $$ \begin{aligned} \text{Average Rate of Change} &= \frac{f(5) - f(1)}{5 - 1} \ &= \frac{-8 - 16}{5 - 1} \ &= \frac{-24}{4} \ &= -6 \end{aligned} $$

(A) $-6$

(B) $-\frac{1}{2}$

(C) $\frac{1}{4}$

(D) $1$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change on Interval" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the function at the interval endpoints

Calculate the average rate of change

Answer: