Find the set of values of x for which:
.
I rearranged it to form:
Therefore critical points of the denominator are x = 2, 3.
It says that the numerator is always positive, could you explain why exactly this is, or is this just something that you "know".
I am not sure then how to work out a set of values for x, they have x<2 and x>3 in the book.
Thanks in advance for the help
Hello,
If the discriminant of a quadratic is negative, then it keeps a constant sign, the same as a.
So here, since a=1, and the discriminant is , the above is always positive.
You can prove it by taking the derivative. For this particular polynomial.
Then, for the quotient to be positive, you need the denominator to be positive.I am not sure then how to work out a set of values for x, they have x<2 and x>3 in the book.
Thanks in advance for the help
The product of two terms is positive if and only if both terms have the same sign.
That is to say [x-2>0 and x-3>0] or [x-2<0 and x-3<0]
From the first one, you have [x>2 and x>3], which is [x>3]
From the second one, you have [x<2 and x<3], which is [x<2]
Does it look clear to you ?