which interval contains a local minimum for the graphed function?

$-4, -2.5$
$-2, -1$
$1, 2$
$2.5, 4$

Question

which interval contains a local minimum for the graphed function?

$-4, -2.5$
$-2, -1$
$1, 2$
$2.5, 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Local Extrema", "Analyzing Graphs" ], "current_concepts": [ "Local Extrema", "Analyzing Graphs" ] } ## Identify local minima from the graph $$ \begin{aligned} &\text{Local minimum 1: } (-0.44, -4.3) \implies x \approx -0.44\ &\text{Local minimum 2: } (3, -4) \implies x = 3 \end{aligned} $$ ## Check which interval contains a local minimum x-value $$ \begin{aligned} &[-4, -2.5] \implies \text{No local minimum } x\text{-value in this interval}\ &[-2, -1] \implies \text{No local minimum } x\text{-value in this interval}\ &[1, 2] \implies \text{Contains local maximum at } x = 1.7 \text{ but no local minimum}\ &[2.5, 4] \implies \text{Contains local minimum at } x = 3 \text{ since } 3 \in [2.5, 4] \end{aligned} $$

(A) $[-4, -2.5]$

(B) $[-2, -1]$

(C) $[1, 2]$

(D) $[2.5, 4]$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Analyzing Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Identify local minima from the graph

Check which interval contains a local minimum x-value

Answer: