2006-10-22 04:03:38 · 7 answers · asked by Olivia 4 in Science & Mathematics ➔ Mathematics
It's false because all you know is that f(a) is EITHER a local minimum OR a local maximum OR a constant value in that vicinity.
Aloha
2006-10-22 04:05:50 · answer #1 · answered by Anonymous · 2⤊ 0⤋
False. It would be a relative maximum.
If f''(a) < 0, the curve opens downward. So the point at which its tangent is 0 (f'(a) = 0) is a high point, with the curve going downward on both sides of that point.
2006-10-22 04:07:28 · answer #2 · answered by actuator 5 · 0⤊ 0⤋
f(x) give you the function
f'(x) defines the slope of that function
if the slope is 0 then you have a high low or saddle point
f''(x) defines the curvature or slope of the slope
if f''(x) < 0 at a point then the curvature opens up downwards it defines a maximum
if f''(x) > 0 at a point then the curvature opens up upwards it defines a minimum
if f''(x) = 0 you have a saddle point (well that is what we call them in Europe) which is neither a max nor a min point
2006-10-22 04:17:50 · answer #3 · answered by Toby_Wan_Kenoby 2 · 0⤊ 0⤋
False, it has a maximum at X=a. If it has to be mimimum then f ''(a)>0.
2006-10-22 04:13:09 · answer #4 · answered by Mathew C 5 · 0⤊ 0⤋
false
its maxima.
it represents a parabola opening downwards.Hence, it has noi minima and vertex is point of maxima
2006-10-22 04:15:29 · answer #5 · answered by lovingnitin 2 · 0⤊ 0⤋
True.
2006-10-22 04:05:41 · answer #6 · answered by Viktor 3 · 0⤊ 0⤋
nooooooo it is maximum at x=a
2006-10-22 04:05:43 · answer #7 · answered by AD 1 · 1⤊ 0⤋