3.3.65
3 parts | 0 of 1 point

find the average rate of change of $f(x) = -3x^2 + 4$ over each of the following intervals.

(a) from $-1$ to $1$
(b) from $2$ to $4$
(c) from $3$ to $6$

part 1 of 3

Question

3.3.65
3 parts | 0 of 1 point

find the average rate of change of $f(x) = -3x^2 + 4$ over each of the following intervals.

(a) from $-1$ to $1$
(b) from $2$ to $4$
(c) from $3$ to $6$

part 1 of 3

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change" ] } ## Calculate the average rate of change from -1 to 1 $$ \begin{aligned} &f(x) = -3x^2 + 4\ &f(1) = -3(1)^2 + 4 = 1\ &f(-1) = -3(-1)^2 + 4 = 1\ &\text{Rate} = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{1 - 1}{2} = 0 \end{aligned} $$ ## Calculate the average rate of change from 2 to 4 $$ \begin{aligned} &f(4) = -3(4)^2 + 4 = -44\ &f(2) = -3(2)^2 + 4 = -8\ &\text{Rate} = \frac{f(4) - f(2)}{4 - 2} = \frac{-44 - (-8)}{2} = \frac{-36}{2} = -18 \end{aligned} $$ ## Calculate the average rate of change from 3 to 6 $$ \begin{aligned} &f(6) = -3(6)^2 + 4 = -104\ &f(3) = -3(3)^2 + 4 = -23\ &\text{Rate} = \frac{f(6) - f(3)}{6 - 3} = \frac{-104 - (-23)}{3} = \frac{-81}{3} = -27 \end{aligned} $$ ## Question a The average rate of change from $-1$ to $1$ is $0$. ## Question b The average rate of change from $2$ to $4$ is $-18$. ## Question c The average rate of change from $3$ to $6$ is $-27$. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the average rate of change from -1 to 1

Calculate the average rate of change from 2 to 4

Calculate the average rate of change from 3 to 6

Answer:

Question a

Question b

Question c