SOLUTION: Find the maximum or minimum value of f(x)= -3x^2 +4x-1

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Question 201168This question is from textbook Intermediate algebra an applied approach
: Find the maximum or minimum value of f(x)= -3x^2 +4x-1 This question is from textbook Intermediate algebra an applied approach

Found 2 solutions by Earlsdon, RAY100:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the maximum/minimum of:
f%28x%29+=+-3x%5E2%2B4x-1 If you were to graph this quadratic equation, you would see that the resulting curve is a parabola that opens downward (also indicated by the negative coefficient of the first term), and this means that the vertex of the parabola will occur at the maximum point on the curve.
To find the value of the x-coordinate of this point, use:
x+=+%28-b%29%2F2a where, for this equation, a = -3, and b = 4, so...
x+=+%28-4%29%2F2%28-3%29
highlight%28x+=+2%2F3%29 and to find the value of the y-coordinate, you just substitute x+=+2%2F3 into the given equation and solve for y (after replacing f(x) with y).
y+=+%28-3%29x%5E2%2B4x-1 Substitute x+=+%282%2F3%29
y+=+-3%282%2F3%29%5E2%2B4%282%2F3%29-1 Evaluate.
y+=+-3%284%2F9%29%2B%288%2F3%29-1
y+=+-4%2F3%2B8%2F3-3%2F3
highlight%28y+=+1%2F3%29 This is the value of the y-coordinate of the vertex (maximum).
The maximum point (the vertex) on the curve (a parabola) occurs at (2%2F3,1%2F3)
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-3x%5E2%2B4x-1%29

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
y= -3x^2 +4x -1
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differentiate and set equal to zero
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y' = -6x +4
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-6x +4 =0
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-6x =-4
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x= 2/3,,,,,,,
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substitute into original eqn
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y = -3(2/3)^2 +4(2/3) -1
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y= -3 (4/9) +8/3 -3/3
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y= -4/3 +8/3 -1/3
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y = 1/3,,,,,,,,
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Checking points in proximity, ( 0,-1) and (1,0) confirm a downward pointing y parabola , with a vertex at (2/3,1/3) which is a max
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