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Find the largest value of c such that -2 is in the range of .x^2 + 3x + c - 7x + x^2

 Jul 20, 2022
 #1
avatar+14084 
+1

The largest value of c such that -2 is in the range of .x^2 + 3x + c - 7x + x^2 is 0.

\(c=-2x^2+4x-2\\ \frac{dc}{dx}=-4x+4=0\\ x=1\\ c=-2\cdot 1^2+4\cdot 1-2\\ \color{blue}c=0\)

laugh  !

 Jul 20, 2022
edited by asinus  Jul 20, 2022
edited by asinus  Jul 20, 2022
 #2
avatar+124676 
+1

x^2  + 3x  + c - 7x + x^2   =  -2

 

2x^2 - 4x + c  =  -2

 

[2x^2 - 4x + 2] + c  =  0

 

The  parabola  2x^2 - 4x + 2   has its vertex at  [ 4] / [ 2*2 ] =  1

And the y value here is  0

So  c =  0

 

cool cool cool

 Jul 20, 2022

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