Question

Find the critical numbers of the function g(y)=y−1/y²-3y³

A) y=−1
B) y=0
C) y=1
D) y=±1

Answer 1

To find the critical numbers of the function g(y) = y - 1/y² - 3y³, we can solve the derivative of g(y) for zero or undefined values. The critical numbers are y = -1, y = 0, y = 1, and y = ±1.

Step-by-step explanation:

To find the critical numbers of the function g(y) = y - 1/y² - 3y³, we need to find the values of y where the derivative of g(y) is equal to zero or undefined.

1. First, find the derivative of g(y) using the power rule and quotient rule: g'(y) = 1 + 2/y³ - 9y².
2. Set g'(y) equal to zero and solve for y: 1 + 2/y³ - 9y² = 0.
3. After simplifying the equation, we get a quadratic equation: 9y^5 - y^2 - 2 = 0.
4. Use factoring, the quadratic formula, or a graphing calculator to solve for the critical numbers.
5. The critical numbers of the function g(y) are the values of y that make g'(y) zero or undefined.
6. In this case, the critical numbers are:
   A) y = -1
   B) y = 0
   C) y = 1
   D) y = ±1.