+818 Find the smallest integer c such that the domain of the function f(x)=x2+1x2−x+c+3x2−7x is all real numbers.
+130466 The denominator cannot = 0
Simplifying the denominator we get
4x^2 -8x + c → this is an upward turning parabola
To have a domain of all real numbers, this parabola must lie above the x axis
So.....the discrimiant must be < 0 ....so....
(-8)^2 -4(4) ( c) < 0
64 - 16c < 0
64 < 16c
4 < c
So
c > 4
The smallest integer is 5
