SOLUTION: Hi! {{{f(x)= -(4/3)x^2 + 12x}}} Can you prove that: if {{{ a<b<=9/2 }}} so we have {{{f(a)<f(b)}}} Whith that, I'll determine the slope of the function. I tried at fir

Algebra ->  Functions -> SOLUTION: Hi! {{{f(x)= -(4/3)x^2 + 12x}}} Can you prove that: if {{{ a<b<=9/2 }}} so we have {{{f(a)<f(b)}}} Whith that, I'll determine the slope of the function. I tried at fir      Log On


   



Question 412400: Hi!
f%28x%29=+-%284%2F3%29x%5E2+%2B+12x
Can you prove that: if +a%3Cb%3C=9%2F2+ so we have f%28a%29%3Cf%28b%29
Whith that, I'll determine the slope of the function.
I tried at first to calculate f(b)-f(a), but I don't know what to do after that...
Thank you and sorry for bad English.



Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
When x+%3C+9%2F2, the function has a positive slope, since the vertex is at 9/2 and the x^2 coefficient is negative. We can say that the function is *strictly increasing* on this interval, so if a+%3C+b+%3C=+9%2F2, then f%28a%29+%3C+f%28b%29.