Benjamin753 Posted September 23, 2005 Share Posted September 23, 2005 Hi anybody... I have a problem. Someone (or most) should find it really easy, but I'm having trouble. Here it is. f(x)= x^(1/3) (or the cube root of x) need to find f'(x) using limit as h->0 of (f(x+h) - f(x))/h Now, I already know what the answer is: (1/(3(x^(2/3))), but how do I get that using the difference quotient (above). Obviously, my algebra skills are rusty, but here is what I did to get the wrong answer: ((x+h)^(1/3)) - (x^(1/3)) ( times the conjugate) ------------------------ h ((x+h)^(2/3)) + (x^(2/3)) ------------------------- ((x+h)^(2/3)) + (x^(2/3)) = x + h - x --------------------------- h((x+h)^(2/3)) + (x^(2/3)) = 1 ---------------------------- ((x+h)^(2/3)) + (x^(2/3)) (then sub 0 for h, because it is a limit problem) then ----> f'(x) = 1 ------------ 2(x^(2/3)) which is not correct... Anybody help me out with this one?? I would appreciate it! Thanks! Link to comment Share on other sites More sharing options...
Benjamin753 Posted September 23, 2005 Author Share Posted September 23, 2005 Nevermind... I got it... my conjugate was wrong... oops. Link to comment Share on other sites More sharing options...
Dave Posted September 23, 2005 Share Posted September 23, 2005 FYI, there was a complete thread on this here. Link to comment Share on other sites More sharing options...
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