Hey, I am taking a test tommorrow on extrema, concavity, and optimization. Also, the Rolle's Theorem and Mean Value Theorem will be on it. What is the easiest way to keep the MVT and RT separate?
2007-06-24 08:39:09 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Rolle's is a special case of the MVT, where the derivative in question is zero. See:
http://en.wikipedia.org/wiki/Rolles_theorem#Generalizations
That should help you keep them straight, since you really only have to remember the MVT.
2007-06-24 08:51:05 · answer #1 · answered by сhееsеr1 7 · 0⤊ 1⤋
Rolle's Theorem requires f(a)= f(b) = 0 to guarantee that there will be at least one value of x in the interval a<= x<=b, for which the derivative is 0.
The mean value theorem is a generalization of Rolle's Theorem and does not require f(a)=f(b)= 0. It states that if f(x ) is continuous and has a derivative at each value of x in a<=x<=b, then there will be at least one point x1 in this interval where f(b)-f(a) = (b-a)f'(x1).
2007-06-24 16:13:43 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
RT is a special case of the MVT that only applies when the two points are intersecting the x-axis.
2007-06-24 15:54:38 · answer #3 · answered by Alex 1 · 0⤊ 0⤋
u are speaking another language to me my friend..
2007-06-24 15:43:17 · answer #4 · answered by chichibaby 5 · 0⤊ 2⤋