Question

Consider the function f(x) = x³-3x²+2x+1. To find the horizontal tangent line, one needs to:

A) Set f‵(x) =0
B) Set f(x) =0
C) Set f‵‵(x) =0
D) Set f‵(x) =1

Answer 1

To find a horizontal tangent line, set the first derivative (f‵(x)) equal to zero, matching option A.

Step-by-step explanation:

To find the horizontal tangent line for a function, you need to first calculate the derivative of the function, which will give you a formula for the slope of the tangent line at any point on the function.

The horizontal tangent line occurs where the slope is zero, since a horizontal line has a slope of zero. Therefore, you should set the first derivative of the function (f‵(x)) equal to 0 in order to find where the slope of the tangent line is horizontal. This corresponds to option A)