Please explain how to solve. **Instructions:**Use the graph of \( f'(x) \) shown to identify a possible graph of \( f(x) \).**Graphs Explanation:**- **Top Graph (f'(x)):** - The graph depicted is of the derivative \( f'(x) \) shown in red. - The graph appears to increase steeply and then levels off as \( x \) increases beyond a certain point. - It shows distinct behavior changes particularly around the origin.**Possible Graphs for f(x):**1. **Bottom Left (Green Graph):** - Exhibits a decrease until around \( x = -3 \), then steadily increases. - Negligible variation around the origin suggests local extremum behavior. 2. **Bottom Middle (Yellow Graph):** - Displays an initial decrease, transitioning to a gradual increase as \( x \) becomes positive. - Features a more gradual slope transition compared to the first option.3. **Bottom Right (Purple Graph):** - Starts with an increase, steeply rises past the origin, and continues to increase as \( x \) increases. - Represents a consistent positive slope behavior across the range.4. **Top Right (Blue Graph):** - Generally exhibits a downward concave parabola-like shape. - Shows reciprocal behavior to the derivative’s decreasing trend to zero.**Considerations:**- Analyze the zero crossings and slope changes in \( f'(x) \) to correspond these with local minimums and maximums in \( f(x) \).- The relation between areas where \( f'(x) \) is positive or negative, indicating where \( f(x) \) is increasing or decreasing, will aid in identifying the correct graph. **Problem:**Find the equation of the tangent line to the curve \( f(x) = x^2 + 2x \) at \( x = 1 \).Enter the answer in the box.\[ T(x) = \square \]**Solution Approach:**To find the equation of the tangent line, follow these steps:1. **Differentiate the function**: Find the derivative \( f'(x) \) to determine the slope of the tangent line at any point \( x \).2. **Evaluate the derivative at \( x = 1 \)**: This will give the slope of the tangent line at the specific point \( x = 1 \).3. **Calculate the y-coordinate of the point**: Substitute \( x = 1 \) into the original function to find \( f(1) \).4. **Use point-slope form to find the equation**: The tangent line's equation can be written in the form \( y - f(a) = f'(a)(x - a) \), where \( a = 1 \) in this case.Following these steps will yield the equation for \( T(x) \).

Given: f(x)=x2+2x at x=1 To find the equation of the tangent line.

Answered: Find the equation of the tangent line…

Find the equation of the tangent line to the curvef (x) = x- + 2x at x = 1. Enter the answer in the box.

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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