SOLUTION: I am given the equation f(x)=300x-11x squared +2. I am asked to find the maximum. Normally the homework problems show step by step instruction although this one isn't. Can you plea

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Question 946390: I am given the equation f(x)=300x-11x squared +2. I am asked to find the maximum. Normally the homework problems show step by step instruction although this one isn't. Can you please help we with this
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your function is f(x)=300x-11x^2+2, restatable as f(x)=-11x^2+300x+2.
Adding the proper rendering tags, f%28x%29=-11x%5E2%2B300x%2B2.

The function f is a parabola opening downward, therefore having a maximum. If f has real
roots, they can be used for finding the symmetry axis, and from it, the maximum of f.

Not clear which method you are allowed here. One way is, complete the square to put into
standard form. The other way is, find the roots of f, find the midpoint of those roots, and
use that value to find corresponding f.

I will start this using Completing The Square, which might possibly not be the easiest way.

-11x%5E2%2B300x%2B2
-11%28x%5E2-%28300%2F11%29x-2%2F11%29
-11%28x%5E2-%28300%2F11%29x%2B%28150%2F11%29%5E2-2%2F11-%28150%2F11%29%5E2%29
-11%28%28x-150%2F11%29%5E2-2%2F11-%28150%2F11%29%5E2%29
-11%28%28x-150%2F11%29%5E2-22%2F11%5E2-150%5E2%2F11%5E2%29
-11%28%28x-150%29%5E2-%2822%2B150%5E2%29%2F11%5E2%29
Now distrubute the previously factored Negative Eleven.
highlight%28-11%28x-150%29%5E2%2B%2822%2B150%5E2%29%2F11%29

Now the equivalent form of your function is highlight%28f%28x%29=-11%28x-150%29%5E2%2B%2822%2B150%5E2%29%2F11%29
and I have simply not finished the computation for the constant term. The vertex for the
maximum point is at highlight%28x=150%29, highlight%28highlight%28y=%2822%2B150%5E2%29%2F11%29%29, this being the maximum value.


You may need to study or review how to Complete The Square, and also about Standard Form for a parabola.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I am given the equation f(x)=300x-11x squared +2. I am asked to find the maximum. Normally the homework problems show step by step instruction although this one isn't. Can you please help we with this
These sure are some big numbers that don't seem to cancel. Are you sure you submitted the problem correctly?

f%28x%29+=+300x+-+11x%5E2+%2B+2_____f%28x%29+=+2+%2B+300x+-+11x%5E2

The maximum occurs at the x coordinate of the vertex, or at x+=+-+b%2F%282a%29, or x+=+-+300%2F%282+%2A+-+11%29, or x+=+%28-+300%29%2F%28-+22%29, or x+=+150%2F11

f%28x%29_or_y+=+2+%2B+300x+-+11x%5E2 

f%28x%29_or_y+=+2+%2B+300%28150%2F11%29+-+11%28150%2F11%29%5E2 ----- Substituting x+=+150%2F11, where the maximum occurs 

f%28x%29_or_y+=+2+%2B+%2845000%2F11%29+-+11%2822500%2F121%29 

f%28x%29_or_y+=+2+%2B+%2845000%2F11%29+-+%2822500%2F11%29 

f%28x%29_or_y+=+%2822%2F11%29+%2B+%2845000%2F11%29+-+%2822500%2F11%29 

Maximum occurs at: f%28x%29_or_y+=+22522%2F11, or highlight_green%28y+=+2047.454545%29 ≈ 2047.45

You can do the check!! 

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