Let `f(x) =ax^(2) -b|x|`, where a and b are constants. Then at x = 0, f (x) is

Options

A. maximized whenever `a gt 0, b gt 0`
B. maximized whenever `a gt 0, b lt 0`
C. minimized whenever `a gt 0, b gt 0`
D. minimized whenever `a gt 0, b lt 0`

Answer

To find the value of \( f(x) \) at \( x = 0 \) for the function \( f(x) = ax^2 - b|x| \), we will follow these steps:

### Step 1: Substitute \( x = 0 \) into the function
We start by substituting \( x = 0 \) into the function \( f(x) \).

\[ f(0) = a(0)^2 - b|0| \]

### Step 2: Simplify the expression
Now, we simplify the expression obtained from the substitution.

\[ f(0) = a(0) - b(0) = 0 - 0 = 0 \]

### Conclusion
Thus, the value of \( f(x) \) at \( x = 0 \) is:

\[ f(0) = 0 \]