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Find the maximum value of 4*sin(x)^2 - 12*sin(x) + 7.

 Dec 17, 2019
 #2
avatar+106519 
+1

y  = 4sin^2(x) -  12sin (x)  +  7

 

Take the derivative and set to 0

 

y '=  8sinxcosx   - 12cosx  = 0

 

So

 

8sinx cos x  -  12cos x  =  0      factor

 

4cos (x)  ( 2sin (x)  - 3)  = 0       set each factor to 0  and solve for x  and we have that

 

x  = pi/2  or 3pi/2    sin x  =  3/2  ( this is not possible )

 

So....the max occurs at   x  = 0

 

At  pi/2  the function value is

 

4sin^2(pi/2) - 12 sin(pi/2)  +  7   =   -1

 

At (3pi/2)  the function value  is 

 

4sin^2 (3pi/2) - 12 sin (3pi/2)  +  7  =

 

4  + 12  +  7   =     

 

23   =   the max value

 

 

cool cool cool

 Dec 17, 2019

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