The Purplemath Forums

Okay so the question is asking to show that for 0<x<y, sqrty - sqrtx < (y - x)/(2 sqrt x) (using the mean value theorem) I think I have some valuable information pertaining to the question...but I am so confused about how to solve it I could just be pulling numbers out of nowhere in a desperate atte...

Thanks for the response! But I am not sure what I am supposed to do with this f(t) = sqrt t ... how does that fit in with the question? Am I using substitution with the t?

...so.. the derivative of c, which is 1/2sqrt c should equal the slope of the tangent, sqrt y/ y. It makes sense in theory, but how do I make them equal eachother? Am I now supposed to solve for one of the variables? But there is two of them. I do not understand the next step. Thanks for your help s...

Soo... can I designate numbers to the value of x and y as long as they fit in with 0<x<y? How do I know which numbers to use to do that?

okay so, the f(y)-f(x)/y-x has to be greater than 0, which means that b-a > 0 which means that the divisor must be positive so that the answer stays above zero, so b>a! I don't need to find an exact answer, do I?!

I mean , so y>x...but i just realized that that is what the 0<x<y was saying anyways. nevermind. I am still confused!

I have read over both of my math texts many times, I am just really having difficulty with this concept. I understand the theory behind it, that if a function satisfies the two conditions then the slope of the tangent = f'(c) for some c on the interval of the function (a,b), but having a hard time a...

Thank you for your help! So glad I finally understand it.