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What is the maximum value of $4(x + 7)(2 - x)$, over all real numbers $x$?

 Mar 19, 2020
 #1
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+1

4 ( x + 7) ( 2 - x)      expand

 

4 ( -x^2  - 7x + 2x  + 14)

 

4 ( -x^2  - 5x  + 14)

 

-4x^2  - 20x  + 56

 

The  max value occurs  at  x  = - (-20)  / [ 2 (-4) ]  =  20 / -8   =  - 5/2  = -2.5

 

Plugging this into the original function we find the  max  as

 

4( -2.5 + 7) ( 2  -  -2.5)  =

 

4 ( 4.5) ( 4.5)   = 

 

81

 

 

cool cool cool

 Mar 19, 2020

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