 # Question: Can A Tangent Line Be Horizontal?

## What is horizontal tangent line?

A horizontal tangent line is a mathematical feature on a graph, located where a function’s derivative is zero.

This is because, by definition, the derivative gives the slope of the tangent line.

Horizontal lines have a slope of zero..

## What does it mean when the tangent line is vertical?

A tangent of a curve is a line that touches the curve at one point. … It has the same slope as the curve at that point. A vertical tangent touches the curve at a point where the gradient (slope) of the curve is infinite and undefined. On a graph, it runs parallel to the y-axis.

## How do you find where a tangent line is horizontal?

To find the points at which the tangent line is horizontal, we have to find where the slope of the function is 0 because a horizontal line’s slope is 0. That’s your derivative. Now set it equal to 0 and solve for x to find the x values at which the tangent line is horizontal to given function.

## How do you find the tangent line of a curve?

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

## How do you find a vertical tangent or cusp?

2 Answers. The definition of a vertical cusp is that the one-sided limits of the derivative approach opposite ±∞: positive infinity on one side and negative infinity on the other side. A vertical tangent has the one-sided limits of the derivative equal to the same sign of infinity.

## How do you find where a tangent line is parallel?

To be parallel, two lines must have the same slope. The slope of the tangent line at a point of the parabola is given by the derivative of y=x2−3x−5. This means that the question is asking at what point the derivative of the parabola will equal the slope of 3x−y=2.

## Can a tangent line be vertical?

In mathematics, particularly calculus, a vertical tangent is a tangent line that is vertical. Because a vertical line has infinite slope, a function whose graph has a vertical tangent is not differentiable at the point of tangency.

## How do you find the normal line of a tangent line?

The normal line is defined as the line that is perpendicular to the tangent line at the point of tangency. Because the slopes of perpendicular lines (neither of which is vertical) are negative reciprocals of one another, the slope of the normal line to the graph of f(x) is −1/ f′(x).

## What is the tangent of a straight line?

Tangent, in geometry, straight line (or smooth curve) that touches a given curve at one point; at that point the slope of the curve is equal to that of the tangent. A tangent line may be considered the limiting position of a secant line as the two points at which it crosses the curve approach one another.

## Is a horizontal tangent line differentiable?

The function is differentiable at a point if the tangent line is horizontal there. In contrast, vertical tangent lines exist where the slope of a function is undefined. The function is not differentiable at a point if the tangent line is vertical there.