Discussion
If \(f(x) = x|x|\), then \(f'(-10)\)=
Answer: D
\(f'(-10)\) equals 20.
For \(x \lt 0\), \(|x| = -x\), so \(f(x) = -x^{2}\) and \(f'(x) = -2x\). At \(x = -10\):
\[ f'(-10) = -2(-10) = 20 \]
In general \(f'(x) = 2|x|\), which is never negative, so the negative options are impossible; 40 doubles the derivative.
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