Exercise · ZW-DERIVATIVE-017 · ★★☆ Intermediate
For \(f(x)=x|x|\), what is \(f'(0)\)?
Choose one option.
Show answer
- A. \(0\)
Explanation
The difference quotient is \(h|h|/h=|h|\), which tends to \(0\). Unlike \(|x|\), here the derivative does exist at the origin.
Review the concept: Derivative
The derivative of \(f\) at \(a\) is the limit of the difference quotient as \(h\to0\). It measures the instantaneous rate of change and is the slope of the tangent line at \((a,f(a))\).
\[f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}\]
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