so you want f(x) > g(x), right?
-4x^4+6x(4x-1)-4 > -3x^2((x^2)-8)-6x-5
That is,
-4x^4+6x(4x-1)-4 - (-3x^2(x^2-8)-6x-5) > 0
-x^4+1 = 0
-(x-1)(x+1)(x^2+1) > 0
-1 < x < 1
That is, fewer than 1000 games
Unity Games is a company that sells video games. Its revenue last year was modelled by the function g(x)=-4x^4+6x(4x-1)-4 and its revenue this year is modelled by the function f(x)=-3x^2((x^2)-8)-6x-5 where x is the number of video games sold in the thousands and the revenue is in millions of dollars. Determine the range of values for the number of video games sold that makes the revenue this year greater than the revenue last year. You must use a full algebraic solution.
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