Question 1205103
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The revenue function for a particular product is R(x)= x(4-0.0001x).How to Find the largest possible revenue.
to solve this do I just have to find the critical point and check if its the maximum point using the derivative?
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<pre>
This way of finding critical point of the derivative is one of possible ways to solve
the problem, but it assumes that the student knows basic of Calculus.


There are other ways that require knowledge of basics of Algebra, ONLY.


This function  R(x) = x*(4-0.0001x) is a quadratic function, which has x-intercepts at
x= 0 and x= {{{4/0.0001}}} = 40000.  Hence, it has the maximum half-way between the x-intercepts,
which (half-way) is  {{{(0+40000)/2}}} = {{{40000/2}}} = 20000.


Now, to find the largest possible revenue, simply substitute x= 20000 into the formula for R(x)
and get

    {{{R(x)[max_]}}} = 20000*(4-0.0001*20000) = 40000.


<U>ANSWER</U>.  {{{R(x)[max_]}}} = 40000.
</pre>

Solved.


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There are other simple Algebra ways to solve this problem (and million other similar problems).


See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>

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