The range of the function g(x) = 2/(2 + 4x + 3x^2) can be written as an interval (a,b]. What is a+b?
+128475 We have a lower power polynomial over a higher power polynomial
This produces a horizontal asymptote of y = 0
This is the bottom of the range
To discover the max use some Calculus
Take the first derivative of the function and set = 0
0 - 2 * (4 + 6x)
____________ = 0
(2 + 4x + 3x^2)
This simplifies to
4 + 6x = 0
4 = -6x
x = -4/6 = -2/3
The max occurs at x = -2/3
The max is 2 / ( 2 + 4(-2/3) + 3(-2/3)^2 ) = 2 / [ 2 -8/3 + 4/3 ] = 2 / [ 2/3] = 3
The range is (0, 3 ]
a + b = 0 + 3 = 3
