Exercise · ZW-DERIVATIVE-008 · ★☆☆ Basic
Which limit defines the derivative of \(f\) at \(a\)?
Choose one option.
Show answer
- B. \(\lim_{h\to0}\frac{f(a+h)-f(a)}{h}\)
Explanation
The derivative is the limit of the difference quotient: the difference of values divided by h. Dropping the division or adding instead of subtracting gives a different expression.
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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