Question

Please show all work. Thank you!

2. Sections 4.3,4.5,4.6 Graphing:Consider the function f (x) = sin(2x) + cos(2x)on the interval [0, 1]. For this question, give your answers to parts a,b,c in interval notation. a. Find the intervals on which f is increasing or decreasing b. Find the local maximum and local minimum values of f c. Find the intervals of concavity d. Give the inflection points (if any) e. Sketch the graph of f. Be sure to label and scale your axes, which are straight lines.

Answer 1

f (w) Sin (2x) + cos (2x) [., a f(x) = sin(2x) + COS(22)) d (sin (2x)) + Šx (cos(2x)) Cos (2x) (2) + - Sin (2x) (2) f(x) 2 Cos (2x) zsin (2x) too acos (2x) esin (2x) acos (22) = 2 Sin Sin (2x) tan (2x) = 1 22= 7 tan x = s Solutia Ranse [ot] ſ x = 5T 8 Critical Points coithin drain = 5T s ca < 55 8 8 tenetia marsten Interiels are os xu T x < 77 ST 5T <x<T osx<T 8 te = acos (22) asin (2x) 2 zł (5) - 2005 (2) - asin (29) <x< SI 8 f (7) = 2coshta 3 esin (265) = 0.246 70 (positive) = -2.7320 40 (negatie) ST くんく 8 22 ST 6 t'l ) - 20051233) - 2S (27) = 2.732030(Panitie) Interval of Increasing ( ou (st, I) Decreasing interval ST

Put entrene points in tw)=sin(2x) + cos2x) Sin (215)) + Cos(2(T) = 2 x - T 8 t() x= 5T f(3) = sin(2)) + COS( 2(32)). - local maxinum ( Local Minimum 57 f(x) = ( 2008 (2W - 2 sin (2x) f (x) - 4 Sin (22) – 4 Cos(22) 4 sin (2x) – 4 Cos(22) = 0 tan (2x) 3T + Ton 4 x = 3T & TO x = 3T 8 x=7T 8 Inthechien points in emain Intervals 3T 8 X= 7T 8 function t(a) Sign 3T <aL7T 7T ocal 3T 8 o<x<3 < x ST 8 x=7 f(a) = - 4 sin (22) - -4Cos(2x) t() = -4 Sin (245)) - 4200 (2 (7) = -1.464120 (negative) +") = -450/2C%)-460%) = 1 46+1>o (positie) 31 Rc7K 8 x =5T 6 7T tact 8 (T) -4 sin ( 2(A)) -4 Cos (2(T) = -4 co negatics x = T Concave up wasd ( 37 77 Concave Downward (0, 317) u (77 IT

Put Intlection points มา (x) = Sin (2x) + Cos (2x) 37 +(अ) = Sin(AP)) + as (2C))0 a ग (8) = 30()+ ces ((2)) = 0 Inthection points (x,y) 27 8 (5 17 2 Y