To find the critical numbers of the function g(y) = y² + 2y + 4, we need to first compute its derivative and then set that derivative equal to zero.
The derivative of the function, denoted as g'(y), is obtained using the power rule:
g'(y) = 2y + 2
Next, we set the derivative equal to zero to find the critical points:
2y + 2 = 0
Solving for y gives:
2y = -2
y = -1
Thus, the critical number for the function is y = -1.
In summary, the only critical number of the function g(y) = y² + 2y + 4 is y = -1. This point is where the function may have a local maximum, local minimum, or a point of inflection.