1. Determine for which values of x each function from to is differentiable and find the derivative. (a) f (x) = | x – 1 | (b) f (x) = | x2 – 1 | (c) f (x) = | x | (d) f (x) = x | x | 2. Let f (x) =...

1. Determine for which values of x each function from

to

is differentiable and find the derivative.

(a) f (x) = | x – 1 | (b) f (x) = | x²
– 1 |

(c) f (x) = | x | (d) f (x) = x | x |

2. Let f (x) = x²
sin (1/x²) for x ≠ 0 and f (0) = 0.

(a) Show that f is differentiable on
.

(b) Show that f ′ is not bounded on the interval [ – 1, 1].