# Homework Help: Help on a differentiability prob.

1. Oct 27, 2004

### ziddy83

hey guys, whats up. Its my first time posting so yeah....

Ok i'm attempting to do the following problem...

let f(x) = x^3 for x is less than or eqaul to 4.
(6x^2)-8x when x is greater than 4

i need to see if f(x) is differentiable at x = 4. I tried it through the definition of the derivative as a function. For the first part im using x^3 and plugging it into f(x) in the def. of the deriv. and i cant seem to figure out what to do with the h I have in the exponent and in the denomenator. i fot as far as....

x^3 lim (a^h-1)/h....I know what x is, 4...but what do i do with the a and the h? please someone help, thanks.

2. Oct 27, 2004

### vsage

Not sure how you would accomplish what you're doing easily with your problem but I would personally see if the derivative at x = 4 was the same at both functions. Note the function is differentiable at a point x if the limit of the function from the positive side is the same as the limit of the function from the negative side.