Answer to Question #252628 in Calculus for Jimmy

Question

Find all points where f fails to be differentiable. Justify your answer.

(a) f(x) = |3x − 2| (b) f(x) = |x^(2) −2|

Answer 1

(a) $f(x)=3x-2,\;\;x>\frac{2}{3}.$

$f(x)=2-3x,\;\;x<\frac{2}{3}.$

f(x) is not differentiable at the point $(\frac{2}{3},0)$.

(b) $f(x)=x^2-2, \;\;x<-\sqrt{2} \;or\; x>\sqrt{2}$.

$f(x)=2-x^2 ,\;\;-\sqrt{2}<x<\sqrt{2}$ .

f(x) is not differentiable at the points $(-\sqrt{2},0)$ and $(\sqrt{2},0).$