Ira S. answered • 03/11/16
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y=x^(2/3) is a graph you should memorize. When you have an even numerator and an odd denominator, and the numerator is less than the denominator......4/5, 4/7, 2/9, etc......you always get a cusp. At a cusp, like a corner, there is no derivative...but everywhere else on the graph, it is differentiable.
You can tell when you have a cusp because f(x) is defined, but f'(x) is not defined.
An asymptote is when f(x) is undefined and f'(x) is also undefined.
so y=x^(2/3) is defined for all x
but y' = (2/3) x^(-1/3) or y' = 2/(3x^.33333333) which is undefined at x=0.....so there's a cusp at x=0 and defined everywhere else.
Hope this helped.
Ira S.
A fractional expression is undefined when the numerator is a non zero number and the denominator is zero.....5/0 0r -12/0.....so your derivative is undefined when 3x^(1/3) = 0 ( the denominator is 0) which is when x = 0. You get what i'm saying?
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03/12/16
Pia R.
Oh okay i have to substitute the numbers on the domain to the x on the derivative! Thank u so much!
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03/12/16
Ira S.
I;\'m not sure you get it....y' = 45/(x-5) is undefined when x=5 since the denominator will be 0. y' = 1/(x2-16) is undefned when the denominator is 0...which is when x=plus or minus 4......Got me?
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03/12/16
Pia R.
So for the closed interval that I have, how do I know that it is not differentiable? Solely because of the graph is that right? Im so confused im sorry
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03/12/16
Ira S.
find the trouble spots....if your interval does not contain the trouble spot numn
bers, then it will be differentiable. If it does all hell breaks loose.. If your interval was from 2 to 14, there is no problem...if your interval contains zero, in your case, there's a problem. so find the problem numbers.
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03/12/16
Pia R.
Okay one last thing, what am I solvng for this part? A fractional expression is undefined when the numerator is a non zero number and the denominator is zero.....5/0 0r -12/0.....so your derivative is undefined when 3x^(1/3) = 0 ( the denominator is 0) which is when x = 0. You get what i'm saying?
Report
03/12/16
Pia R.
03/12/16