Question
ind all \( x \)-values (if any) where the graph of the function \( f(x)=3 x^{2}-6 x \) has a horizontal tangent line. Separate multiple answers with a comma. If the tangent line is lever horizontal, write NA for your answer.
Ask by Greene Davison. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
x = 1
Solution
To find where the function has a horizontal tangent line, first compute the derivative, which represents the slope of the tangent line:
f(x) = 3x² - 6x
f '(x) = 6x - 6
A horizontal tangent line occurs when f '(x) = 0.
Set 6x - 6 = 0 and solve for x:
6x = 6
x = 1
Thus, the graph has a horizontal tangent at x = 1.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the \( x \)-values where the graph of the function \( f(x) = 3x^2 - 6x \) has a horizontal tangent line, we first need to calculate the derivative \( f'(x) \). The derivative is given by: \[ f'(x) = 6x - 6. \] A horizontal tangent line occurs where the derivative is equal to zero: \[ 6x - 6 = 0. \] Solving for \( x \): \[ 6x = 6 \] \[ x = 1. \] Therefore, the function has a horizontal tangent line at \( x = 1 \). So, the solution is: 1.
