Find the stationary points of the function 3x2 - y² + x
Answers
Answer:
please mark me as brainlist
Step-by-step explanation:
There are four features of particular interest on the surface. At point A there is a local maximum,
at B there is a local minimum, and at C and D there are what are known as saddle points.
At A the surface is at its greatest height in the immediate neighbourhood. If we move on the surface
from A we immediately lose height no matter in which direction we travel. At B the surface is at its
least height in the neighbourhood. If we move on the surface from B we immediately gain height,
no matter in which direction we travel.
The features at C and D are quite different. In some directions as we move away from these points
along the surface we lose height whilst in others we gain height. The similarity in shape to a horse’s
saddle is evident.
At each point P of a smooth surface one can draw a unique plane which touches the surface there.
This plane is called the tangent plane at P. (The tangent plane is a natural generalisation of
the tangent line which can be drawn at each point of a smooth curve.) In Figure 7 at each of
the points A, B, C, D the tangent plane to the surface is horizontal at the point of interest. Such
points are thus known as stationary points of the function. In the next subsections we show how to
locate stationary points and how to determine their natu