How do you show the x-axis is tangent to the curve?

A line parallel to the x-axis will have slope m=0. So you need to take the first derivative, and set it equal to zero to solve for the x values at which the slope of the tangent to your curve is zero. In your case, slope being zero, your equation(s) will be given by y=y0.

What are the tangent to the curve x cube Y cube is equal to 3 xy at the origin?

Mathematics Question Therefore, 3axy = 0, which gives x = 0 and y = 0 as two tangents to the curve at origin.

How do you find an equation of a tangent line at a given point?

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.

What does it mean to be tangent to the x-axis at the origin?

If a graph is tangent to the x-axis, the graph touches but does not cross the x-axis at some point on the graph.” Based on that, was your initial assessment correct? We also know that if the graph is tangent to the x-axis at some point (in this case the origin, x = 0) the slope is 0 at that point.

How do you work out tangent?

In order to find the equation of a tangent, we:

1. Differentiate the equation of the curve.
2. Substitute the value into the differentiated equation to find the gradient.
3. Substitute the value into the original equation of the curve to find the y-coordinate.
4. Substitute your point on the line and the gradient into.

How do you find the radius of curvature at the origin?

We get x′=0 and x″=4. Therefore the curvature at the origin is κ=|x″|(1+x′2)32=4.

What is a tangent point?

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. The word “tangent” comes from the Latin tangere, “to touch”.

Can you have a tangent to the x-axis?

X-axis is a straight line and therefore, one cannot have a tangent to x-axis. It would mean that the tangent and the x-axis will be coincident at all points and this goes against the very definition of tangent.

How do you find the tangent of a straight line?

In short you can’t find the tangent of straight line. The X- axis is the straight line with slope=0, the equation of X – axis is y=0 , therefore the slope dy/dx =0 so there is no tangent for x – axis because the tangent touch the curve at one point so, there is no tangent to X-axis Seniors using loophole to save for retirement.

How do you write a tangent equation on a normal vector?

This, in turn, means that provided →r u ×→r v ≠ →0 r → u × r → v ≠ 0 → the vector →r u ×→r v r → u × r → v will be orthogonal to the surface S S and so it can be used for the normal vector that we need in order to write down the equation of a tangent plane.

How to find the tangent point of an ellipse?

By adding semi major/minor axes $ (3,2) $to the center of ellipse x,y coordinates $ (-1,2) $ , you know where your tangent points are. Share Cite Follow edited Dec 4 ’14 at 18:50