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A curve is defined by x³y² = x. The graph of this curve is shown below along with a sketch of the tangent line to the curve at the point (-1,1). y (a). Use the diagram to estimate the slope of the tangent line to the graph of this curve at the point (-1,1). Show your steps and explain your strategy. (b). Use Implicit Differentiation to determine the formula for . Show your steps and use proper dx notation. (c). Use the formula obtained in Part (b) to determine the exact slope of the tangent line.

A curve is defined by x³y² = x. The graph of this curve is shown below along with a sketch of the tangent line to the curve at the point (-1,1). y (a). Use the diagram to estimate the slope of the tangent line to the graph of this curve at the point (-1,1). Show your steps and explain your strategy. (b). Use Implicit Differentiation to determine the formula for . Show your steps and use proper dx notation. (c). Use the formula obtained in Part (b) to determine the exact slope of the tangent line.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A curve is defined by x3y2 = x. The graph of this curve is shown below along with a sketch of the tangent line to the curve at the point (-1,1). y (a). Use the diagram to estimate the slope of the tangent line to the graph of this curve at the point (-1,1). Show your steps and explain your strategy. (b). Use Implicit Differentiation to determine the formula for Show your steps and use proper dx notation. (c). Use the formula obtained in Part (b) to determine the exact slope of the tangent line.
Transcribed Image Text:A curve is defined by x3y2 = x. The graph of this curve is shown below along with a sketch of the tangent line to the curve at the point (-1,1). y (a). Use the diagram to estimate the slope of the tangent line to the graph of this curve at the point (-1,1). Show your steps and explain your strategy. (b). Use Implicit Differentiation to determine the formula for Show your steps and use proper dx notation. (c). Use the formula obtained in Part (b) to determine the exact slope of the tangent line.
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