Over which interval is the graph of f(x) = -x² + 3x + 8 increasing?

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}

It is given that function is 

f(x) = -x² + 3x + 8

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

-2x + 3 > 0

-2x > -3

x < 3/2 or 1.5

Therefore, the graph is increasing over (∞, 1.5)

Over which interval is the graph of f(x) = -x² + 3x + 8 increasing?

Summary:

Over (∞, 1.5), the graph of f(x) = -x² + 3x + 8 is increasing.