f(x)= { ((x^2 x≤1)),(),((∣x−2∣ x>1)) :} find the critical points


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Question Number 70741 by aliesam last updated on 07/Oct/19
$f(x)= { ((x^2 x≤1)),(),((∣x−2∣ x>1)) :} find the critical points$
$f (x) = {\begin{cases} x^{2} x ⩽ 1 \\ ∣ x - 2 ∣ x > 1 \end{cases}$ $f i n d t h e c r i t i c a l p o i n t s$
Commented bykaivan.ahmadi last updated on 07/Oct/19
$f(x)= { ((x^2 x≤1)),((2−x 1<x<2)),((x−2 x≥2)) :} f′(x)= { ((2x x≤1)),((−1 1<x<2)),((1 x>2)) :} f′(x)=0⇒2x=0⇒x=0 is a critical point f′(1),f′(2) are not exist so they are critical points$
$f (x) = {\begin{cases} x^{2} x ⩽ 1 \\ 2 - x 1 < x < 2 \\ x - 2 x ⩾ 2 \end{cases}$ $f^{'} (x) = {\begin{cases} 2 x x ⩽ 1 \\ - 1 1 < x < 2 \\ 1 x > 2 \end{cases}$ $f^{'} (x) = 0 \Rightarrow 2 x = 0 \Rightarrow x = 0 i s a c r i t i c a l p o i n t$ $f^{'} (1), f^{'} (2) a r e n o t e x i s t s o t h e y a r e c r i t i c a l p o i n t s$
Commented byaliesam last updated on 07/Oct/19

$f^{'} (1) = ?$
Commented byaliesam last updated on 07/Oct/19

Commented bykaivan.ahmadi last updated on 07/Oct/19

$y o u a r e r i g h t$
Commented byaliesam last updated on 07/Oct/19

$o k s i r a n d t h a n k y o u f o r t h e s o l u t i o n$
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