SOLUTION: Hello, I'm having trouble with functions. I'm given f(x)=x^2-4x+16 and g(x)= -0.5x^2+4x+10. How do I find the longest interval, starting at x=1, over which g(x)-f(x) is incr

Algebra ->  Functions -> SOLUTION: Hello, I'm having trouble with functions. I'm given f(x)=x^2-4x+16 and g(x)= -0.5x^2+4x+10. How do I find the longest interval, starting at x=1, over which g(x)-f(x) is incr      Log On


   

Question 841112: Hello,
I'm having trouble with functions. I'm given f(x)=x^2-4x+16 and g(x)= -0.5x^2+4x+10.
How do I find the longest interval, starting at x=1, over which g(x)-f(x) is increasing?
Thank you so much!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

-0.5x^2+4x+10

-(x^2-4x+16)

 -1.5x^2 + 8x - 6  |Recommend putting this in vertex form by completing the square

Increasing prior to the vertex point...

 +%28-3%2F2%29%28x-8%2F3%29%5E2+%2B+14%2F3+   V(8/3, 14/3)