Question

if f(x) = 0, what does that mean with respect to the tangent line?
tangent line has a negative slope
tangent line is horizontal
tangent line is vertical
tangent line has a positive slope

Explanation:

The derivative \( f^{\prime}(x) \) represents the slope of the tangent line to the graph of \( y = f(x) \) at the point \( x \). If \( f^{\prime}(x)=0 \), by the definition of slope (which is \( m = \frac{\Delta y}{\Delta x} \), and when \( m = 0 \), \( \Delta y=0 \) for any non - zero \( \Delta x \)), the tangent line has a slope of zero. A line with a slope of zero is a horizontal line.

Answer:

Tangent line is horizontal