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What is the maximum value of 4(x + 7)(12 - x)?

 Jan 24, 2022
 #1
avatar+516 
+2

First we open the parenthesis.

\(4(-x^2 +5x + 84)\)

 

Then we open up parenthesis again.

\(-4x^2 + 20x + 336\)

 

When x = 0, the value is 336.

When x = 1, the value is 352.

When x = 2, the value is 360.

When x = 3, the value is also 360.

 

But we see when x = 2.5, the value is 361. 

If x = 2.4, the value is 360.96

If x = 2.6, the value is 360.96.

So that means the medium value for x is 2.5, which makes the expression the maximum value.

For the maximum value of the expression, it is 361.

 

smiley

 Jan 24, 2022
 #2
avatar+36417 
+1

4(x + 7)(12 - x)    expand to:

-4x^2 + 20x + 336           max will occur at   x  =  - b/2a   =  -20 /(2(-4)) = 2.5

 

sub in that value in the equation  to find the max is   361

 Jan 24, 2022

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