SOLUTION: What is the maximum value of the function f(x) = (3-x)(5x + 35)?

Algebra ->  Rational-functions -> SOLUTION: What is the maximum value of the function f(x) = (3-x)(5x + 35)?      Log On


   

Question 149596: What is the maximum value of the function f(x) = (3-x)(5x + 35)?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, we need to find the zeros.


%283-x%29%285x+%2B+35%29=0 Set the expression equal to zero.



Now set each factor equal to zero:

3-x=0 or 5x+%2B+35=0

Now solve for x for each factor:

x=3 or x=-7

So the zeros of %283-x%29%285x+%2B+35%29 are x=3 or x=-7



Now average the zeros to get %283%2B%28-7%29%29%2F2=%28-4%29%2F%282%29=-2


So the axis of symmetry (ie the x-coordinate of the vertex) is x=-2


Now plug in x=-2 to find the y coordinate of the vertex


f%28x%29=%283-x%29%285x+%2B+35%29 Start with the given function.



f%28-2%29=%283-%28-2%29%29%285%28-2%29+%2B+35%29 Plug in x=-2


f%28-2%29=%283%2B2%29%285%28-2%29+%2B+35%29 Rewrite 3-%28-2%29 as 3%2B2


f%28-2%29=%283%2B2%29%28-10+%2B+35%29 Multiply


f%28-2%29=%285%29%2825%29 Add


f%28-2%29=125 Multiply


So the y coordinate of the vertex is y=125


This means that the vertex is at the point (-2,125). Since the vertex is either the highest or lowest point (in this case the highest), this means that that the maximum value of the function is 125