Question

If \( f(x) = x^3 + bx^2 + cx + d \) and \( 0<b^2<c \), then in \( (-\infty, \infty) \),

• A. \( f(x) \) is a strictly increasing function
• B. \( f(x) \) has local maxima
• C. \( f(x) \) is a strictly decreasing function
• D. \( f(x) \) is bounded

Hint:

The derivative test helps to determine the monotonicity of a function. If the derivative is positive, the function is increasing.

Answer 1

The Correct Option is A

Given the condition \( 0<b^2<c \), the derivative of \( f(x) \) will indicate that it is a strictly increasing function.
Final Answer: \[ \boxed{f(x) \text{ is a strictly increasing function}} \]