9) Find the open interval(s) on which the function x) cor(7x) is increasing in t
ID: 2884398 • Letter: 9
Question
9) Find the open interval(s) on which the function x) cor(7x) is increasing in the interval (0, 1.795) (p) Round numerical values in your answer to three decimal places ? increasing on: (0.224, 1.449), (0673, os98). C2.1 22, 1340, (1.571, 1.795) increasing on: (0.673, 0.898), (1.122, 1346), (1.571, 1.795), (0.224, 0.449) ? increasing on: (0S98, 1.122), (0449, 0.673), ( 1.346, 1.571). (O, 1.795) increasing on: (0, 0.224). (0.449, 0.673), (0.898, 1.122). (1.346, 1571) increasing on: (0.224, 0.449. (0.573, 0.398). (1.122, 1.340, (1571. 1.795) Section 4 10) Determine the open intervals on which the graph of y -8r3+2x1+5x-2 is concave downward or (ps) concave upward. Oconcave downward on (-, o) ? concaveupwardonl-oo, ?concave downward onl?? cocave upward onl.?concave downward onl .«I con ave upward onl-. ?coe ave downward onl? concave downward on 00, 12concaveuard on 12. concave downward on I-oo, T concave upward ??, oc ·T?F concave downward on??. oo 11) Determine the open intervals on which the graph of )- 6cost is concave downward or (Ups) concave upward c ave downward on (T.-???)?. ?)- concave downward on -- --.- concave upward on (-2,-??1-2.27(T.2 concave downward on ..", (-_.-4). ( concave upward on (-_,-??1-4. 4RT, concave upward on (4.!)(7.?)?. ; concave downward on (-??-t5W??)- 4'4 4 *4 (-_-_)- M)(5? 7? concave downward on concave upward on .. 6666
Explanation / Answer
9. f(x) = cos2(7x)
f '(x) = -2*7 * cos(7x) sin(7x) = -7 sin(14x)
Critical number, f '(x) =0
-7 sin(14x) =0
sin(14x)=0
x = 0 , 0.224 ,0.449 , 0.673 , 0.898 , 1.122, 1.346 ,1.571.
In (0, 0.224), f'(x) is negative
In (0.224,0.449), f '(x) is positive
In (0.449, 0.673) , f '(x) is negative
In (0.673,0.898) , f '(x) is positive
In (0.898,1.122) , f'(x) is negative
In (1.122,1.346) , f '(x) is positive
In(1 .346,1.571), f '(x) is negative
In (1.571,1.795) , f '(x) is positive
So increasing interval , (0.224,0.449),(0.673,0.898) ,(1.122,1.346), (1.571,1.795)
Decreasing interval(0,0.224),(0.449, 0.673) ,(0.898,1.122),(1 .346,1.571)
Correct option is Last option
10 .f(x) = -8x3+2x2+5x-2
f'(x) = -24x2+4x +5
f ''(x) = -48x +4
Inflection point , f ''(x) =0
-48 x+4 =0
x = 1/12
In (-inf,1/12), f ''(x) >0
In (1/12, inf), f''(x) <0
Concave up (-inf,1/12), concave down (1/12, inf)
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