Answer to Question #254028 in Calculus for Anuj

Question #254028

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|


1
Expert's answer
2022-01-25T10:09:29-0500

a)

f(x)=3x2f(x)=3x-2 for x>2/3x>2/3

f(x)=(3x2)f(x)=-(3x-2) for x<2/3x<2/3

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

MATLAB command:

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



b)

f(x)=x22f(x)=x^2-2 for x>2|x|>\sqrt2

f(x)=(x22)f(x)=-(x^2-2) for x<2|x|<\sqrt2

f(x) is not differentiable at x=±2x=\pm\sqrt2

MATLAB command:

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




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