Find the largest value of c such that -2 is in the range of .x^2 + 3x + c - 7x + x^2
The largest value of c such that -2 is in the range of .x^2 + 3x + c - 7x + x^2 is 0.
\(c=-2x^2+4x-2\\ \frac{dc}{dx}=-4x+4=0\\ x=1\\ c=-2\cdot 1^2+4\cdot 1-2\\ \color{blue}c=0\)
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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
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