Over which interval is the graph of f(x) = x² + 5x + 6 increasing?

Solution:

Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis.

Increasing and decreasing functions are also called non-decreasing and non-increasing functions

It is given that function is 

f(x) = x² + 5x + 6

We know that graph of f(x) is increasing if f’(x) > 0

2x + 5 > 0

2x > -5

x > -5/2 or -2.5

Therefore, the graph is increasing over  (- 2.5, ∞)

Over which interval is the graph of f(x) = x² + 5x + 6 increasing?

Summary:

Over  (- 2.5, ∞), the graph of f(x) = x² + 5x + 6 is increasing.