- At which points is \( g(x) = |x| \) differentiable?
- Show that \( g'(x) = x/|x| \).
- Use the chain rule to find a formula for \( \frac{d}{dx}(|f(x)|) \),
and then use it to find the derivative of \( h(x) = |x^{2}-4| \) at \( x = 1 \).
- Can \( \frac{d}{dx}(|f(x)|) \) exist at a point where \( f(x) = 0 \)?
Tags: diff, chain-rule, absolute-value, quadratic, computation, generalization, multistep, a--a, t1, c2
This is a great problem! It’s worth the time spent because students get to use the chain rule to simplify their lives.
– Concha Gomez 1999-02-19