determine all critical points for the function.

\f(x) = -3x^2 + 2x^3\

$x = $
(use a comma to separate answers as needed.)

Question

determine all critical points for the function.

\f(x) = -3x^2 + 2x^3\

$x = $
(use a comma to separate answers as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Power Rule" ], "new_concepts": [ "Critical Points" ], "current_concepts": [ "Power Rule", "Critical Points" ] } ## Find the derivative of the function $$ \begin{aligned} f(x) &= -3x^2 + 2x^3 \ f'(x) &= \frac{d}{dx}(-3x^2 + 2x^3) \ f'(x) &= -6x + 6x^2 \end{aligned} $$ ## Set the derivative to zero and solve for x $$ \begin{aligned} -6x + 6x^2 &= 0 \ 6x(x - 1) &= 0 \ x = 0 \quad &\text{or} \quad x = 1 \end{aligned} $$ Determine all critical points for the function $f(x) = -3x^2 + 2x^3$. $x =$ $0, 1$ (Use a comma to separate answers as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Critical Points" ] }

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Question

Explanation:

Find the derivative of the function

Set the derivative to zero and solve for x

Answer: