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Find the slope of the tangent line to the curve - 3x² + 4xy - 2y³ = at the point (3,-2). - 35

Find the slope of the tangent line to the curve - 3x² + 4xy - 2y³ = at the point (3,-2). - 35

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Find the slope of the tangent line to the curve: \[ -3x^2 + 4xy - 2y^3 = -35 \] at the point \((3, -2)\). **Instructions:** To find the slope of the tangent line to the given curve at the specified point, you will need to use implicit differentiation. First, differentiate both sides of the equation with respect to \(x\), remembering to apply the product rule to the term \(4xy\) and the chain rule to the term \(-2y^3\). Then, solve for \(\frac{dy}{dx}\), which represents the slope of the tangent line at any point on the curve. Finally, substitute \(x = 3\) and \(y = -2\) into the expression for \(\frac{dy}{dx}\) to find the specific slope at the given point. **Graph/Diagram Explanation:** There are no graphs or diagrams provided in this image. The main focus is on differentiating the given implicit equation to find the slope of the tangent line at the indicated point.
Transcribed Image Text:**Problem Statement:** Find the slope of the tangent line to the curve: \[ -3x^2 + 4xy - 2y^3 = -35 \] at the point \((3, -2)\). **Instructions:** To find the slope of the tangent line to the given curve at the specified point, you will need to use implicit differentiation. First, differentiate both sides of the equation with respect to \(x\), remembering to apply the product rule to the term \(4xy\) and the chain rule to the term \(-2y^3\). Then, solve for \(\frac{dy}{dx}\), which represents the slope of the tangent line at any point on the curve. Finally, substitute \(x = 3\) and \(y = -2\) into the expression for \(\frac{dy}{dx}\) to find the specific slope at the given point. **Graph/Diagram Explanation:** There are no graphs or diagrams provided in this image. The main focus is on differentiating the given implicit equation to find the slope of the tangent line at the indicated point.
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