1-f-x-sinx-pi-2-lt-x-2pi-cosx-0-x-pi-2-then-find-the-f-pi-2-2-f-x-sinx-pi-2-lt-x-2pi-cosx-0-x-pi-2-then-find

Question Number 195180 by mustafazaheen last updated on 26/Jul/23

1 . f (x) = {\begin{cases} sinx, \frac{π}{2} < x ⩽ 2 π \\ cosx, 0 ⩽ x ⩽ \frac{π}{2} \end{cases}

then find the f^{^{'}} (\frac{π}{2}) = ?

2 . f (x) = {\begin{cases} sinx, \frac{π}{2} < x ⩽ 2 π \\ cosx, 0 ⩽ x ⩽ \frac{π}{2} \end{cases}

then find the f^{'} (2 π) = ?

Answered by mathlove last updated on 26/Jul/23

f^{^{'}} (x) = {\begin{cases} c o s x \\ - s i n x \end{cases}

f^{^{'}} (\frac{π}{2}) = - s i n \frac{π}{2} = - 1

f^{^{'}} (2 π) = c o s 2 π = 1

Commented by MM42 last updated on 26/Jul/23

T h e f u n c t i o n i s n o t c o n t i n u o u s e i n

x = \frac{π}{2} . t h e r e f o r e i t i s n o t d i f f e r e n t i a b l e i n x = \frac{π}{2}

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