Differentiable piecewise function

**thedoctor818** · March 3rd 2010, 09:17 AM

My task is as follows:
Let $f(x) = x^2 \text{for } x \geq 0 \wedge f(x) = 0 \text{for } x < 0.$
B. Show that f is differentiable at $x = 0.$
C. Calculate $f' \text{on } \mathbb{R}.$

Any help will be greatly appreciated.

-the Doctor

**Drexel28** · March 3rd 2010, 12:12 PM

Originally Posted by thedoctor818

My task is as follows:
Let $f(x) = x^2 \text{for } x \geq 0 \wedge f(x) = 0 \text{for } x < 0.$
B. Show that f is differentiable at $x = 0.$
C. Calculate $f' \text{on } \mathbb{R}.$

Any help will be greatly appreciated.

-the Doctor

I don't understand. It's clearly differentiable on $\mathbb{R}-\{0\}$ and $\lim_{x\to0^-}\frac{f(x)-f(0)}{x-0}=\lim_{x\to 0^-}0=0=\lim_{x\to0^+}2x=\lim_{x\to0^+}\frac{f(x)-f(0)}{x-0}$

**thedoctor818** · March 3rd 2010, 04:44 PM

Since the $lim_{x\to0-}=lim_{x\to0+}$ then does that mean that $f(x) \; \text{is differentiable at } x=0$ ?

Thread: Differentiable piecewise function

LinkBack

Thread Tools

Display

Differentiable piecewise function

Similar Math Help Forum Discussions

Question about finding the limit of a piecewise function of a piecewise function?

Continuous function differentiable everywhere other than zero, differentiable at zero

Express an absolue value function as a piecewise function

Making a piecewise function differentiable.

Piecewise differentiable equations

Search Tags