Over which interval is the graph x^2+3x+8 increasing

F (x) = x^2+3x+8

now, the pending of the tangent line is d/dx f (x)

f' (x) = 2x + 3

now, we need know when the pending is increasing.

so

2x + 3> 0

solving

x>-3/2

The interval over which the function f (x) = x^2+3x+8 is increasing is (-3/2, + ∞)