1. ## Derivative question

I don't know how to find where the derivative exists or where it fails to exists? and where all the points exists for these functions?
(btw its suppose to be a big parentheses holds both functions)

f(x)={ (x-1)^3, x≥1 and x^3-3x+2, x<1 }

2. Originally Posted by popcandy
I don't know how to find where the derivative exists or where it fails to exists? and where all the points exists for these functions?
(btw its suppose to be a big parentheses holds both functions)

f(x)={ (x-1)^3, x≥1 and x^3-3x+2, x<1 }
1. show f(x) is continuous at x = 1 using the three-part definition of continuity at a point. then ...

2. show f(x) is differentiable at x = 1 using the definition of a derivative at a specific point ... you'll need to show

$\displaystyle \lim_{x \to 1^-} \frac{f(x) - f(1)}{x-1} = \lim_{x \to 1^+} \frac{f(x) - f(1)}{x-1}$