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answer and explanation please

Exam 2 - Password ready - Mat >> problem33.pdf x + → C w ebassign.net/web/Student/Assignment-Responses/submit?dep=23484596&tags#autosave question3851334 5 10. - 5 POINTS LARCALC11 3.3.047.0/2 Submissions Used Consider the function on the interval (0, 2). f(x) = 5 sin?(x) + 5 sin(x) (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-valde) (x,y) - ( (larger x-value) relative minima (x, y) = ( (smaller x-value) (X,Y)= ( (larger x-value) Submit Answer Viewing Saved Work Revert to Last Response

Answer 1

- Page 1) f(x) = 5 sin?x + 5 sinx ,10,21 ) f'in) (f(no] - [5 sin’a +5 din x] (5 sin?n) + ( 5 dinx) f'(X) = 5 sim (2x) + 5 Cos (0) for critical points , f'(2)=0 =) 5 sin (2n) + 5 cos(x)=0 =) RF, = ,4-3, hata but in interval (0,20), n= I is present so, (n= h is critical point sign of f(n) Hve) (tve) summary of monotone intervals behavior :- I okna a/2 n=1/ 2 ² <x<2a sign tve 0 +ve Behavior ) Increasing I saddle increasing f(n) = 5 sin u + 5 sina at usum finds +(1/2) = 10 so, f'(x) is the same sign on both sides of n=4 so, u=h is neither a relative maxime nor relative Minima interval where Increasing (0 ) u( 127) internal where decreasing nowhere in the interval (0,25) No relative Maxima, no relative minime boz at critical point n a e is saddle point