Question

If \( f(x) = a^2 - 1 \), \( x^3 - 3x + 5 \) is a decreasing function of \( x \in R \), then the set of possible values of \( a \) (independent of \( x \)) is:

• A. \( [1, \infty) \)
• B. \( (-1, \infty) \)
• C. \( [-1, 1] \)
• D. \( (-\infty, 1] \)

Hint:

For a decreasing function, use the derivative test to find the possible values of parameters.

Answer 1

The Correct Option is C

Step 1: Analyze the function.
For the function to be decreasing, we need to determine the conditions on \( a \) and the corresponding values of the function. After solving, we find that \( a \) must be between -1 and 1.
Thus, the correct answer is (3).