let $y = 3x^2 + 8x + 4$. if $dx = \delta x = 0.1$ at $x = 1$, use linear approximation or differentials to estimate $\delta y$.

$\delta y =$

Question

let $y = 3x^2 + 8x + 4$. if $dx = \delta x = 0.1$ at $x = 1$, use linear approximation or differentials to estimate $\delta y$.

$\delta y =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Differentials" ], "new_concepts": [], "current_concepts": [ "Differentials", "Linear Approximation" ] } ## Find the differential dy $$ \begin{aligned} y &= 3x^2 + 8x + 4 \ \frac{dy}{dx} &= 6x + 8 \ dy &= (6x + 8) \, dx \end{aligned} $$ ## Evaluate dy at the given values $$ \begin{aligned} x &= 1 \ dx &= 0.1 \ dy &= (6(1) + 8) \cdot 0.1 \ dy &= 14 \cdot 0.1 = 1.4 \end{aligned} $$ ## Approximate the change in y $$ \Delta y \approx dy = 1.4 $$ Let $y = 3x^2 + 8x + 4$. If $dx = \Delta x = 0.1$ at $x = 1$, use linear approximation or differentials to estimate $\Delta y$. $\Delta y =$ 1.4 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Differentials" ] }

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Question

Explanation:

Find the differential dy

Evaluate dy at the given values

Approximate the change in y

Answer: