- At what point is the tangent plane to the surface horizontal?
- How do you find a vertical tangent line?
- At what point in the first quadrant is the tangent line horizontal?
- What is the tangent of a straight line?
- How do you find a tangent line on a graph?
- Can a tangent line be horizontal?
- Can a tangent line be vertical?
- Is it possible for this curve to have a horizontal tangent?

## At what point is the tangent plane to the surface horizontal?

The answer is: z=0 .

Remember that an horizontal plane is tangent to a curve in the space in its points of maximum, minimum or saddle.

We can answer in two ways.

The first: this function is the equation of an elliptic paraboloid with concavity upwards..

## How do you find a vertical tangent line?

Set the denominator of any fractions to zero. The values at these points correspond to vertical tangents. Plug the point back into the original formula. If the right-hand side differs (or is zero) from the left-hand side, then a vertical tangent is confirmed.

## At what point in the first quadrant is the tangent line horizontal?

The tangent line is horizontal if y’ = 0. Using the expression for y’ from (a), we see that y’ = 0 when 2y – x2 = 0 (provided that y2 – 2x ≠ 0). x6 = 16×3. Since x ≠ 0 in the first quadrant, we have x3 = 16.

## 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.

## How do you find a tangent line on a graph?

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.

## Can a tangent line be horizontal?

Horizontal tangent lines exist where the derivative of the function is equal to 0, and vertical tangent lines exist where the derivative of the function is undefined.

## 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.

## Is it possible for this curve to have a horizontal tangent?

(d) Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? … No, the curve cannot have a horizontal tangent where it crosses the x-axis.