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3. Find the equation of the tangent line to the curve f (x)= (1+2x)'" at the point (0,1) in point-slope form.

3. Find the equation of the tangent line to the curve f (x)= (1+2x)'" at the point (0,1) in point-slope form.

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 3: Finding the Equation of a Tangent Line** Find the equation of the tangent line to the curve \( f(x) = (1 + 2x)^{10} \) at the point \( (0, 1) \) in point-slope form. --- To solve this problem, you need to follow these steps: 1. **Differentiate \( f(x) \)** to find the slope of the tangent line. 2. **Evaluate the derivative at \( x = 0 \)** to determine the slope at the given point. 3. Use the **point-slope form** of the equation of a line: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the given point and \(m\) is the slope found in step 2. This exercise will help solidify your understanding of derivatives and their application in finding equations of tangent lines to curves.
Transcribed Image Text:**Problem 3: Finding the Equation of a Tangent Line** Find the equation of the tangent line to the curve \( f(x) = (1 + 2x)^{10} \) at the point \( (0, 1) \) in point-slope form. --- To solve this problem, you need to follow these steps: 1. **Differentiate \( f(x) \)** to find the slope of the tangent line. 2. **Evaluate the derivative at \( x = 0 \)** to determine the slope at the given point. 3. Use the **point-slope form** of the equation of a line: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the given point and \(m\) is the slope found in step 2. This exercise will help solidify your understanding of derivatives and their application in finding equations of tangent lines to curves.
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