18What is the correct answer ### Tangent Line Problem**Objective**: Find the equation of the line tangent to the graph of \( f(x) = (5x - 9)(x + 6) \) at the point \((2, 8)\).---### Solution**Given**:- Function, \( f(x) = (5x - 9)(x + 6) \)- Point, \((2, 8)\)**Solution**:The equation of the line tangent to the graph of \( f(x) = (5x - 9)(x + 6) \) at \((2,8)\) is:\[ y = 41x - 74 \]*Type an equation.*---### Explanation of the ProcessTo find the equation of a tangent line, follow these general steps:1. **Find the derivative \( f'(x) \)**: This will give you the slope of the tangent line at any point \( x \).2. **Evaluate \( f'(x) \) at \( x = 2 \)**: Substitute \( x = 2 \) into the derivative to find the slope of the tangent line at the given point.3. **Use the point-slope form of a line**: With the slope from step 2 and the given point, use the point-slope form to find the equation of the tangent line.In this specific example, after differentiation and substitution, the slope at \( x = 2 \) was found to be 41, leading directly to the equation \( y = 41x - 74 \).*Derivation details could be further provided in a complete lesson to guide through each differentiation and substitution step.*

This question is based on application of derivative to find slope of tangent line.

Answered: Find an equation of the line tangent to…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter3: Linear And Nonlinear Functions

Section: Chapter Questions

Problem 26MCQ

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Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+6) at (2,8). The equation of the line tangent to the graph of f(x) = (5x-9)(x+6) at (2,8) is y=41x-74 (Type an equation.)