Final answer:
To find the critical numbers of the function g(y), we calculated its derivative, set it equal to zero, and solved for y. The critical number for g(y) = y - 5y² - 3y + 15 is -1/5.
Step-by-step explanation:
To find the critical numbers of the function g(y) = y - 5y² - 3y + 15, we need to determine the points where the derivative of the function is zero or where the derivative does not exist. First, we calculate the derivative of g(y), which is g'(y) = 1 - 10y - 3. Setting the derivative equal to zero gives us the equation g'(y) = -10y - 2 = 0. Solving this equation for y gives us the critical numbers.
We add 2 to both sides, getting -10y = 2, then divide both sides by -10, yielding y = -1/5. Hence, the critical number of g(y) is -1/5.