Question

Which of the following intervals describes where the function y = 3x^3 - 16x + 2 is increasing?

A. x > 4/3
B. x < -4/3
C. -4/3 < x < 4/3
D. None of the above

Answer 1

The function y = 3x^3 - 16x + 2 is increasing for x > 4/3.

Step-by-step explanation:

To determine where the function y = 3x^3 - 16x + 2 is increasing, we need to find the intervals where the derivative of the function is positive.

Taking the derivative of the function, we get y' = 9x^2 - 16.

Setting y' > 0 and solving for x, we find that x > sqrt(16/9) or x < -sqrt(16/9).

Simplifying, x > 4/3 or x < -4/3. Therefore, the correct answer is A. x > 4/3.