Exercise · ZW-DERIVATIVE-001 · ★☆☆ Basic
The number \(f'(a)\) represents...
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- A. the slope of the tangent line to the graph at (a, f(a))
Explanation
The derivative at a is the limit of the difference quotient and equals the slope of the tangent line at (a, f(a)). It measures the instantaneous rate of change of f at a.
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 \((a,f(a))\).
\[f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}\]
More practice problems: derivative
- ZW-DERIVATIVE-002 If a function is differentiable at a, then...
- ZW-DERIVATIVE-003 Using the limit definition of the derivative, what is f'(2) if f(x)=x^2 + x?
- ZW-DERIVATIVE-004 Using the limit definition of the derivative, what is f'(1) if f(x)=3 x^2 - 2 x?
- ZW-DERIVATIVE-005 Using the limit definition of the derivative, what is f'(2) if f(x)=x^3?
- ZW-DERIVATIVE-006 Using the limit definition of the derivative, what is f'(4) if f(x)=√x?
- ZW-DERIVATIVE-007 Using the limit definition of the derivative, what is f'(2) if f(x)=(1)/(x)?
- ZW-DERIVATIVE-008 Which limit defines the derivative of f at a?
- ZW-DERIVATIVE-009 Let f(x)=|x|. What happens with f'(0)?