Question

What are the critical points of `g(x)=(x+2)/(7-4x)`?

Answer 1

`g(x)` has no critical point and is strictly increasing in its domain.

Explanation:

Critical points are determined as the values of `x` for which the first derivative vanishes, so:

`g'(x) = frac ((7-4x)+4(x+2)) ((7-4x)^2)=15/((7-4x)^2)`

Evidently, the derivative of `g(x)`is always positive and never equals zero, thus `g(x)` has no critical point and is strictly increasing in its domain.

graph{(x+2)/(7-4x) [-10, 10, -5, 5]}