No you don’t. Inserting (2,-1) in the LHS gives 4*2+2(-1) = 8-2 = 6 so the required point is not on that plane.Helloooo said:and have the tangent plane:
4x+2y+3=0
Firstly i noticed an error in my writing.Orodruin said:No you don’t. Inserting (2,-1) in the LHS gives 4*2+2(-1) = 8-2 = 6 so the required point is not on that plane.
That's it, right there:Helloooo said:However i still don´t know how to fint the straight tangent line.
Helloooo said:4x+2y-6=0
Does that mean that the tangent plane and straight tangent line is the same?Orodruin said:That's it, right there:
In two dimensions, a tangent line and the tangent plane are the same thing. In n dimensions the tangent plane has n-1 dimensions. It is a more general concept because it is not restricted to two dimensions.Helloooo said:Does that mean that the tangent plane and straight tangent line is the same?
If so, why are they called differently or is it just in this particulary problem?
I see, thank you so much for your help!Orodruin said:In two dimensions, a tangent line and the tangent plane are the same thing. In n dimensions the tangent plane has n-1 dimensions. It is a more general concept because it is not restricted to two dimensions.
The slope of the tangent line can be found by taking the derivative of the function at the point of interest. This will give you the slope of the tangent line at that specific point.
No, the tangent line must be drawn at a specific point on the curve. This point is known as the point of tangency and is where the tangent line touches the curve at only one point.
The equation for a straight tangent line is y = mx + b, where m is the slope of the tangent line and b is the y-intercept. The slope can be found using the derivative of the function, and the y-intercept can be found by plugging in the coordinates of the point of tangency.
The tangent line should only touch the curve at one point, which is the point of tangency. Additionally, the slope of the tangent line should match the slope of the curve at that point. You can also check your answer by graphing the function and the tangent line to see if they intersect at the point of tangency.
Yes, there is a shortcut called the tangent line approximation or linearization. This method uses the tangent line at a nearby point to approximate the tangent line at the point of interest. It is often used in calculus to simplify calculations and find approximate solutions.