Exercise · ZW-DERIVATIVE-013 · ★☆☆ Basic
Compute \(f'(4)\) for \(f(x)=\sqrt x\).
Choose one option.
Show answer
- D. \(\tfrac14\)
Explanation
\(\dfrac{\sqrt{4+h}-2}{h}=\dfrac{1}{\sqrt{4+h}+2}\to\tfrac14\), after rationalizing the numerator.
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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