1. Let $$f(x) = ax^2 - b|x|$$ , where a and b are constants. Then at x = 0, f(x) is[CAT 2004]
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By: anil on 05 May 2019 02.30 am
$$f(x) = ax^2 - b|x|$$. For x > 0, $$f(x) = ax^2 - bx$$, will be > 0 if a > 0 and b < 0.
For x < 0, $$f(x) = ax^2 + bx$$ will again be > 0 if a > 0 and b < 0.
Therefore, for a > 0 and b < 0, f(x) will attain its minimum value at x = 0.
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For x < 0, $$f(x) = ax^2 + bx$$ will again be > 0 if a > 0 and b < 0.
Therefore, for a > 0 and b < 0, f(x) will attain its minimum value at x = 0.