Final answer:
To find the critical numbers of a function, we derive the function and determine where its derivative is zero or undefined. Upon deriving the given function g(y), the critical point found is not listed in the provided options, indicating there may be an error in the problem or choices.
Step-by-step explanation:
To find the critical numbers of the function g(y) = y - 5y² - 3y + 15, first we need to find the derivative of the function. The critical numbers are the values of y that make the derivative either equal to zero or undefined. Now, let's find the derivative of g(y):
g'(y) = 1 - 10y - 3
Simplifying this we get:
g'(y) = -10y - 2
To find the critical points, we set g'(y) equal to 0:
0 = -10y - 2
10y = -2
y = -2 / 10
y = -1 / 5
As this value is not one of the options provided, it suggests that there might be an error in the original function given or in the response choices.