Answer to Question #252399 in Calculus for Steve

Question

Question 03

Write (and draw the graph of) a function which is

(a) Continuous on all points except at x = 1.

(b) Differentiable on all points except at x = 1.

(c) Non-differentiable at five points x = 1, x = 2, x = 3, x = 4 and x = 5.

Answer 1

a,b)

$y=\frac{1}{x-1}$

c)

$y=\frac{1}{x-1}+\frac{1}{x-2}+\frac{1}{x-3}+\frac{1}{x-4}+\frac{1}{x-5}$