Calculus Help

[CryBoy]

Pinky... All the choices given for the problem are wrong. The answer should be negative. Once again... The first derivative of a function is its slope. The second derivative tells you the concavity of the function. For the function y = (x + (x + x^(1/2))^(1/2))^(1/2)
the slope is always positive at any given value of x. Since the second derivative is never equal to zero for any value of x in this function, there is no inflection point. Hence the graph of the function is always concave downward. Therefore, the answer should be negative.

Go to this site

http://wims.unice.fr/wims/wims.cgi

Do a copy and paste of the function below. Ask it to give you the first and second derivative. I have varified that the first derivative given from that program is correct. Therefore, I assume the second derivative given must be correct.

f(x) = (x + (x + x^(1/2))^(1/2))^(1/2)

I used the first derivative given by that program as a function to enter into my calculator, then find the dy/dx of the first derivative at x = 1. It came out -0.2485201

I have also substituted 1 in the second derivative given from the program and cranked out -0.2485199328

Good luck.

Let me know your professor's solution to this problem.

 

[Glferboy21]

CryBoy I believe you are right.

The last answer I got, -.2511 or whatever, is close to your answer and probably due to rounding errors in my calculations. I trust this answer because I got it from my gf's sister who is a PHD student at Princeton in math. She didn't give me the answer but she gave me the formula and I plugged the numbers. Knowing that you got that answer reassures me that this has to be correct.

 

[pinky]

Must be an error on the test...spent too many hours working on that problem....thank you all for your help
:mj01: