mark the critical points on the following graph.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Critical Points" ], "new_concepts": [], "current_concepts": [ "Critical Points", "Local Extrema" ] } ## Identify local extrema where the derivative is zero $$ \begin{aligned} &\text{Local maximum at } x = -1, \quad y = 3.5 \ &\text{Local minimum at } x = 1, \quad y = 2.5 \end{aligned} $$ ## Determine the coordinates of the critical points $$ \begin{aligned} &\text{Point 1: } (-1, 3.5) \ &\text{Point 2: } (1, 2.5) \end{aligned} $$ The critical points on the graph are located at the local maximum and local minimum: $$(-1, 3.5) \quad \text{and} \quad (1, 2.5)$$ { "elements": [ { "type": "functiongraph", "params": [ { "js": "0.125*x*x*x - 0.375*x + 3", "latex": "0.125x^3 - 0.375x + 3" }, -5, 5 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "point", "params": [ [-1, 3.25] ], "properties": { "name": "(-1, 3.25)", "size": 5, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [ [1, 2.75] ], "properties": { "name": "(1, 2.75)", "size": 5, "color": "#F2557F", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Calculus", "Critical Points" ] }

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Identify local extrema where the derivative is zero

Determine the coordinates of the critical points

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