Question

A differentiable function \( f(x) \) has a relative minimum at \( x = 0 \), then the function \( y = f(x) + ax + b \) has a relative minimum at \( x = 0 \) for

• A. all \( a \) and all \( b \)
• B. all \( b \), if \( a = 0 \)
• C. all \( b > 0 \)
• D. all \( a > 0 \)

Hint:

To find the condition for a relative minimum or maximum, check the first and second derivatives of the function.

Answer 1

The Correct Option is B

For the function \( y = f(x) + ax + b \), the condition for a relative minimum at \( x = 0 \) is that the derivative of the function at that point should be zero.
This implies \( a = 0 \), and \( b \) can take any value.
Therefore, the correct answer is (2).