Given-f-x-sin2x-2cos2x-find-f-pi-4-hence-given-g-x-x-0-x-2-3x-x-2-2-x-3-for-a-total-range-of-0-x-3-sketch-the-graph-for-y-g-x-and-find-the-area-with-makes-with-the-x-axis

Question Number 49703 by Rio Michael last updated on 09/Dec/18

G i v e n f (x) = s i n 2 x + 2 c o s 2 x

f i n d f^{'} (\frac{π}{4})

h e n c e g i v e n g (x) = {\begin{cases} x, 0 ⩽ x ⩽ 2 \\ 3 x - x^{2}, 2 ⩽ x ⩽ 3 \end{cases}

f o r a t o t a l r a n g e o f 0 ⩽ x ⩽ 3 s k e t c h t h e g r a p h f o r y = g (x)

a n d f i n d t h e a r e a w i t h m a k e s w i t h t h e x - a x i s

o t h e r w i s e, f i n d t h e c o m p o s i t e f u n c t i o n g f i n t h e r a n g e

2 ⩽ x ⩽ 3 .