Question

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

Answer 1

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,+∞)