Differentiable Function?

Question

I need some help, please! :[

Well, I need to determine the values of x at which a certain fuction is differentiable. Do I just graph it on my calculator? Or is there an algebraic method?

The equation is:
y= square root (x^2 + 9)

Thank you so much, I really appreciate it!

Answer 1

you can type that equation into a graphing calculator for Y1 and then it will graph it then all you have to do is go back to the main screen and hit the button math, then hit nderiv(. After that shows up hit vars, then Yvars (scroll to the right), then hit enter for Y1 it will appear right after the parenthesis then, after that shows up hit comma then x then comma then x. you will get your answer. or you can type what i just said in for Y2 and it will graph the derivative of the function. then just do a trace and find out at what x value will the derivative equal. Hope that helps.

Answer 2

For a function to be differentiable, you need to prove the function is valid for the domain and you have to prove it is continuous. No, graphing isn't a proof.

You have to be careful with the domain here because you can not have negative value inside the square-root, if you are only dealing with real numbers. So your domain is restricted.

You need to find the range where you have positive radicand. (inside the squre root), then state, for the values indicated, square is a valid function for all real numbers. Square-root is not a valid function for radicant being negative. But for the domain of a range (you find what it is), radicant is either zero or positive, and it is continous. So you can say it is a differntiable function.