Find-a-general-formula-for-m-such-that-f-x-sin-x-sin-x-be-not-differentiable-at-x-m-

Question Number 41101 by ajfour last updated on 02/Aug/18

F i n d a g e n e r a l f o r m u l a f o r m

s u c h t h a t f (x) =∣ \sin x ∣ + \sin ∣ x ∣

b e n o t d i f f e r e n t i a b l e a t x = m .

Commented by tanmay.chaudhury50@gmail.com last updated on 02/Aug/18

Commented by ajfour last updated on 02/Aug/18

g o o d s i r; t h a n k s .

Answered by MrW3 last updated on 02/Aug/18

f (- x) = f (x) \Rightarrow w e o n l y n e e d t o s e e x ⩾ 0 :

f (x) =∣ \sin x ∣ + \sin x

∣ \sin x ∣= \sin x f o r 2 n π ⩽ x ⩽ (2 n + 1) π w i t h n ⩾ 0

∣ \sin x ∣= - \sin x f o r (2 n + 1) π ⩽ x ⩽ (2 n + 2) π

\Rightarrow f (x) = 2 \sin x f o r 2 n π ⩽ x ⩽ (2 n + 1) π

\Rightarrow f (x) = 0 f o r (2 n + 1) π ⩽ x ⩽ (2 n + 2) π

\Rightarrow f (x) i s n o t d i f f e r e n t i a b l e a t x = 2 n π a n d (2 n + 1) π,

s o g e n e r a l l y

\Rightarrow m = k π w i t h k = a n y i n t e g e r

Commented by ajfour last updated on 02/Aug/18

A b s o l u t e l y t r u e, S i r . I h a d d r a w n

t h e g r a p h .

Facebook Tweet Pin