SOLUTION: what is the maximum value of 3x^2 + 7x - 2 if -3 is less than or equal to x, which is less than or equal to 0

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Question 1006079: what is the maximum value of 3x^2 + 7x - 2 if -3 is less than or equal to x, which is less than or equal to 0
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Question asks the maximum value between -3%3Cx%3C0. Find where the vertex is in relation to this interval. A possible way is change the expression into standard form and read the x coordinate of the vertex; and note that the vertex is a minimum point for the quadratic function. You are expecting the MAXIMUM value to be at either x=-3 or x=0, because one of them is likely to be greater than the y-value of the vertex.


3x%5E2+%2B+7x+-+2
3%28x%5E2%2B%287%2F3%29x+%29-2
3%28x%5E2%2B%287%2F3%29x%2B%287%2F6%29%5E2%29-3%287%2F6%29-2
3%28x%2B7%2F6%29%5E2-7%2F2-4%2F2
3%28x%2B7%2F6%29%5E2-9%2F2

The vertex, a minimum value for the function, occurs at x=-7%2F6.

Did you really mean the interval INCLUSIVE, like -3%3C=x%3C=0? If yes, then there are TWO maximum values on this interval, not just one value. Otherwise the answer can only be a limit.

-7%2F6=-1%261%2F6

graph%28300%2C300%2C-4%2C4%2C-6%2C2%2C3x%5E2%2B7x-2%29

The limits for the max value on the interval both are at y=0.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

what is the maximum value of 3x^2 + 7x - 2 if -3 is less than or equal to x, which is less than or equal to 0
Maximum value of: 3x%5E2+%2B+7x+-+2, with -+3+%3C=+x+%3C=+0 is: highlight_green%284%29

This MAXIMUM value occurs when x = - 3