Question

Find all points where f fails to be differentiable. Justify your answer. Also draw the graph of f(x) by using

MATLAB.

(a) f(x) = |3x − 2| (b) f(x) = |x

2 −2|

Answer 1

a)

$f(x)=3x-2$ for $x>2/3$

$f(x)=-(3x-2)$ for $x<2/3$

f(x) is not differentiable at $x=2/3$

MATLAB command:

fplot(@x abs(3x-2))

b)

$f(x)=x^2-2$ for $|x|>\sqrt2$

$f(x)=-(x^2-2)$ for $|x|<\sqrt2$

f(x) is not differentiable at $x=\pm\sqrt2$

MATLAB command:

fplot(@x abs(x^2-2))