Math Is Fun Forum

Luke T

Guest

Mean Value Theorem Hard Q(for me)

Suppose that a function is twice differentiable on [0,4] and that f(1) = f(2) = 0 and f(3) = 1

Show that f''(b) > 0.5 for some point b in (0,4)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Mean Value Theorem Hard Q(for me)

I'd double check to make sure your points are correct.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Luke T

Guest

Re: Mean Value Theorem Hard Q(for me)

Well those are the points the teacher gave us, and he said the final answer is 1/(e-d) where e is between 2 and 3, and d is between 1 and 2. I donno???

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Mean Value Theorem Hard Q(for me)

since
f(1)=f(2)
f'(1+p)=0
0<p<1, note, no "=", if any question, refer to your textbook.

since
f(2)=0, f(3)=1
f'(2+q)= (1-0)/(3-2)=1

0<q<1

So
f"(b)= (1-0)/[(2+q)-(1+p)]

0<(2+q)-(1+p)<2 is musts for p and q, otherwise contradictory

So f"(b)>1/2

Your Professor is a master. S/He teaches you that the the mid thereom requires the "mid" point real MID without being either end by this tricky question.

Have you got it now?

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X'(y-Xβ)=0