Thread: differentiable

Def: Let f be a real-valued function defined on an interval I containing the point c, (we allow the possibilty that c is an endpoint of I) we say that f is differentiable at c (or has a derivative at c) if the limit

lim x->c (f(x) - f(c))/(x-c)
exists and is finite.

A) Use definition above to prove that f'(x) = (1/3)^(-2/3) for x is not equal to 0
B) Show that f is not differentiable at x = 0

Originally Posted by learn18

Def: Let f be a real-valued function defined on an interval I containing the point c, (we allow the possibilty that c is an endpoint of I) we say that f is differentiable at c (or has a derivative at c) if the limit

lim x->c (f(x) - f(c))/(x-c)
exists and is finite.

A) Use definition above to prove that f'(x) = (1/3)^(-2/3) for x is not equal to 0
B) Show that f is not differentiable at x = 0

What function?

the way im reading it, but its prob wrong, is that f can be any real valued function

Originally Posted by ThePerfectHacker

What function?

Originally Posted by learn18

the way im reading it, but its prob wrong, is that f can be any real valued function

Yes, but we need a specific function for part A. You didn't give it to us.

-Dan

Im sorry, I must have just completely lost it
here is the function for a and b

f(x) = x^(1/3) for x element of R

Originally Posted by learn18

Im sorry, I must have just completely lost it
here is the function for a and b

f(x) = x^(1/3) for x element of R

I give you a hint that should help.

[x^(1/3) - a^(1/3)]/ (x-a)

Multiply the numerator and denominator by,

x^(2/3) + a^(1/3) * x^(1/3) + a^(2/3)

This will rationalize the numerator.