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 attempt to feel smart!
I have the slope of the tangent for sqrty - sqrt x = -sqrt y / y and the slope of the tangent for (y - x)/(2 sqrt x) = -(1/2y)/ y But not sure what I do with this information! any help would be amazingly appreciated!
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 so far though!
I'm not sure what you are trying to accomplish with the above post.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?!