Question

Let $f\left(x\right)=a{x}^2-b|x|,$ where a and b are constants. Then at x = 0, f(x) is

• A. Maximized whenever a > 0, b > 0
• B. Maximized whenever a > 0, b < 0
• C. Minimized whenever a > 0, b > 0
• D. Minimized whenever a > 0, b < 0

Answer 1

The correct option is D Minimized whenever a > 0, b < 0

$f\left(x\right)=a{x}^2-bx.$ In this function, $x^2$ and x are always positve.
The value thus depends on a and b. f(1) = a - b. Using different options, we find that a - b will be positive if a > 0 and b < 0.
The minimum value of a positive function is 0. Hence (d) is correct option.