What is the normal to a curve at a point where the derivative is zero?

Question

ScanSolve AI Tutor · Accepted Answer

The question asks about the normal to a curve at a point where $f'(x) = 0$ .

Understand the meaning of $f'(x) = 0$ .
The derivative $f'(x)$ represents the slope of the tangent line to the curve at a given point $x$ . If $f'(x) = 0$ , it means the tangent line at that point is horizontal.
Understand the relationship between a tangent and a normal.
The normal line to a curve at a point is perpendicular to the tangent line at that same point.
Determine the orientation of the normal line.
If the tangent line is horizontal (slope $m_t = 0$ ), then the normal line, being perpendicular to it, must be vertical. The slope of a vertical line is undefined.

The correct option is C.

The normal to a curve at a point where $f'(x) = 0$ is a Vertical line.

Answer