We need to Find dy/dx implicitly and explicitly. Are they equivalent? Use the graph to estimate the slope. **Graph Analysis and Derivative Calculation****Graph Description:**The graph consists of two curves and a tangent line:1. **Curves:** - The **blue curve** represents the function: \[ y = \frac{\sqrt{x^2 + 12}}{2} \] - The **purple curve** represents the function: \[ y = -\frac{\sqrt{x^2 + 12}}{2} \]2. **Tangent Line:** - A **red tangent line** is shown touching the blue curve at the point (2, 2).3. **Axes:** The horizontal axis is labeled \(x\) and the vertical axis is labeled \(y\).**Derivative Calculation:****Implicit Equation:**\[4y^2 - x^2 = 12\]Find \( \frac{dy}{dx} \):- Implicitly, solve for \( \frac{dy}{dx} \).- Explicitly, compute \( \frac{dy}{dx} \) for the function \(y\) expressed in terms of \(x\).**Equivalent Results:**Determine if the implicit and explicit results for \( \frac{dy}{dx} \) are equivalent:- Yes- No**Slope Estimation:**Use the graph to estimate the slope of the tangent line at the labeled point (2, 2). Then verify the result analytically by evaluating \( \frac{dy}{dx} \) at the point.**Enter your calculations:**\[\frac{dy}{dx} = \]The graph provides a visual representation to enhance the understanding of implicit differentiation and the comparison with explicit differentiation methods.

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Consider the following graph. implicitly explicitly dy dx y = dy dx -4 = x² + 12 2 = -2 y Are the results equivalent? Yes No 4 2 1-2 Find dy/dx implicitly and explicitly. (The explicit functions are shown on the graph. Only include the x variable when entering the answer for the explicit result.) 4y² - x² = 12 -4 (2, 2) 2 4 y = - x² +12 2 X Use the graph to estimate the slope of the tangent line at the labeled point. Then verify your result analytically by evaluating dy/dx at the point. dy = dx

Consider the following graph. implicitly explicitly dy dx y = dy dx -4 = x² + 12 2 = -2 y Are the results equivalent? Yes No 4 2 1-2 Find dy/dx implicitly and explicitly. (The explicit functions are shown on the graph. Only include the x variable when entering the answer for the explicit result.) 4y² - x² = 12 -4 (2, 2) 2 4 y = - x² +12 2 X Use the graph to estimate the slope of the tangent line at the labeled point. Then verify your result analytically by evaluating dy/dx at the point. dy = dx

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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