why does a parabola have 3 critical points when finding minimum distance? What do they represent?
A function is given 6-x^2. The point is (0,3). After setting d'(x) to zero I get three critical points 0, -sqrt(2.5) and sqrt(2.5)
- PopeLv 71 month agoFavorite Answer
Did you try graphing it? Even a very rough graph would explain the result.
Here the parabola is the curve y = 6 - x². From point (0, 3) there are three normals, meeting the curve at these three points:
At the first and third points the distance is minimized. The second point is the vertex, representing a local maximum for the distance.
- davidLv 71 month ago
WHY? All given points will NOT have 3 critical points. This given point is on the axis f symmetry of the parabola ... that is why it has 3 crit. points ... 2 are symmetric (because of axis of summetry) the 3rd might be a max or a min dist or neither.
- PhilipLv 61 month ago
f(x) = 6-x^2, f'(x) = -2x, f'(x) = 0 ---> x = 0, tangent line L, say, at P(0,6) has slope = 0.
The point Q(0,3) is on a line M, say, which is normal to f(x) at P. PQ = 3 and is the
minimum distance from Q to f(x).
- ted sLv 71 month ago
my question to you is HOW does a linear function have 3 roots ?....and (0,3) is not on the graph of the function !!! ...TRY AGAIN....ahhh..you have a distance function from ( 0 , 3) to the curve...ignore my comments