Exercise · ZW-DERIVATIVE-018 · ★★☆ Intermediate
The tangent line to \(f(x)=x^2\) at the point with abscissa \(1\) is:
Choose one option.
Show answer
- B. \(y=2x-1\)
Explanation
Since \(f(1)=1\) and \(f'(1)=2\), the line is \(y=1+2(x-1)=2x-1\). The option \(y=2x\) has the right slope but does not pass through \((1,1)\).
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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