Recent content by Moonnstars

I figure now to just subtract the left side from the right, setting the equation to f(x). Then, take the first derivative of it, which is g(x) [2\int0^x g(t) dt - (g(x)2)] To prove f' increases, use the fact that g'\geq 0, demonstrating g(x) increases. So, it can be said that...

I found this problem elsewhere, so I was wondering how to prove a specific part of it to be positive, because my teacher wanted a better explanation of it. http://www.mathlinks.ro/viewtopic.php?t=325915 My questions were posted in the forum there as well. Also, I realize that I misread...

Oops. I misplaced my 2. Thanks. So, I was thinking about the application of the MVT... Any ideas, hints if I am in the right direction, because I did a similar problem that made me work in the opposite direction of this one, using MVT. It read: let a,b be differentiable on \Re and suppose...

I am getting confused a bit. Let's see, the derivative of the integral of g(x) dx is just g(x), right? So, then, with the square on it is it, g2(x)g'(x) ?

Then, just 2g(x)?

If you mean the derivatives of the integrals==> the Fundamental Theorem of Calc., then is not just g(x)^3 and (g(x))^2?

Office_Shredder... So, if I use a simple function of just x, then the derivative of it is... 3x^2 \leq (1)^2 which is not true, if my values for x \geq 0 . Is that what you mean (did I do that right)? Is that the contradiction you were referring to, since that is true when x \leq 0 ?

Thank you Office_Shredder and Mark44. Office_Shredder has it written correctly, the part about the parentheses is correct, but it is g(x) dx, not with t's. Though that shouldn't make a difference, right?? Mark44, thank you as well, your Latex writing of the problem is correct, although it...

Homework Statement I apologize for not knowing how to use Latex, so I will type the problem as it is read... Prove that for all x greater than or equal to 0, we have the integral from 0 to x for [g(x)]^3 dx which is less than or equal to (the integral from 0 to x for g(x) dx)^2...