What is the difference between delta x and dx?

Δx (delta x) is about a secant line, a line between two points representing the rate of change between those two points. That's a "differential" (between the two points).

dx is about a tangent line to one point, representing an instantaneous rate of change. That makes it a "derivative."

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are