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

Algebra.Com
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)   (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, .

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.







Now distrubute the previously factored Negative Eleven.


Now the equivalent form of your function is
and I have simply not finished the computation for the constant term. The vertex for the
maximum point is at , , 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)   (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?

_____

The maximum occurs at the x coordinate of the vertex, or at , or , or , or 

 

 ----- Substituting , where the maximum occurs 

 

 

 

Maximum occurs at: , or  ≈ 2047.45

You can do the check!! 

=================== 

RELATED QUESTIONS


maximum profit a chain store manager has been told by the main office that the daily... (answered by ankor@dixie-net.com)

Problem is F(x) = -(x-2)^2 -7 I need to find the vertex , line of symmetry,... (answered by stanbon)

Hello,

I'm taking Calculus online and have a homework problem I'm having trouble with.  (answered by Alan3354)

This one has me bogged down.

I am attempting to graph and looking at the table.

Is... (answered by consc198)

I am supposed to solve this problem by completing the square: 
(x squared) + 11x +... (answered by LifeDeathnCandy)

The Equation of a Parabolic Curve is given by y = -x^2 + 12. What is the Maximum Area of... (answered by jim_thompson5910)

Suppose that a function y=f(x) is increasing on the interval (-5,2)
a.)Over what... (answered by josgarithmetic)

Good Evening!  I am working on some problems for homework.  

Find all real zeros of... (answered by edjones)

I have some problems I got wrong on my test. Please explain step by step what I should... (answered by stanbon,chitra)