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Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

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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Question
**Problem Statement:** Find the equation of the tangent line to \( y = 2^{x^2 - 5x + 1} \) at \( x = 4 \). **Solution:** \[ y = 12 \ln 2 - 1 \] This equation represents the tangent line to the given function at the specified point. To find the tangent line, you'd typically: 1. Calculate the derivative of the function, which gives the slope of the tangent line. 2. Evaluate the derivative at the given point (\(x = 4\)) to find the slope. 3. Use the point-slope form of a line to find the equation of the tangent line, utilizing the slope and the corresponding \( y \)-value at \( x = 4 \). The solution expresses the final equation of the tangent line based on these calculations.
Transcribed Image Text:**Problem Statement:** Find the equation of the tangent line to \( y = 2^{x^2 - 5x + 1} \) at \( x = 4 \). **Solution:** \[ y = 12 \ln 2 - 1 \] This equation represents the tangent line to the given function at the specified point. To find the tangent line, you'd typically: 1. Calculate the derivative of the function, which gives the slope of the tangent line. 2. Evaluate the derivative at the given point (\(x = 4\)) to find the slope. 3. Use the point-slope form of a line to find the equation of the tangent line, utilizing the slope and the corresponding \( y \)-value at \( x = 4 \). The solution expresses the final equation of the tangent line based on these calculations.
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