Find the range of values of c for which 3x^2 - 9x + c > 2.25 for all values of x.
2006-09-23 03:18:45 · 4 answers · asked by unquenchablethirst 2 in Science & Mathematics ➔ Mathematics
Move the 2.25 over to the LHS of the equation then use the quadratic formula - are you just tying in all of your homework questions? That is called cheating - and you are not helping yourself to learn it.
2006-09-23 03:21:35 · answer #1 · answered by whatthe 3 · 3⤊ 0⤋
That's not a challenge! I've seen much harder.
But if you really want to know, the parabola f(x) = 3x^2 - 9x + c must never cross the horizontal line x = 2.25. The key is in the vertex, found at x = -b/2a. As long as the vertex is above, and the parabola is opened up, or below, and opened down, the two will never meet. So let x = -b/2a, where a=3 and b=-9, the co-efficients of x^2 and x, respectively. Solve for c (and get c>k for some k). Since a=3 is positive, the parabola opens up, and thus, the value for y (or f(x)) will never be smaller. Conclude that if you use a different x, you will get c + L > k for some positive L, so that c > k - L, but we already knew that, because c > k > k-L.
So the range of values is whatever c > k that you get, for some k.
2006-09-23 10:39:18 · answer #2 · answered by Anonymous · 1⤊ 0⤋
Take the derivative - 6x -9 = 0
X = 1.5 establishes the minimum for that function.
Substitute 1.5 back in the equation and solve for c.
2006-09-23 11:16:56 · answer #3 · answered by Anonymous · 1⤊ 0⤋
Yeah do what "WHATTHE" said. You aren't learning n e thing if your getting someone else to solve your homework.
2006-09-23 10:24:09 · answer #4 · answered by Lucy Lu 4 · 3⤊ 0⤋