Exercise · ZW-TANGENT-LINE-009 · ★★★ Advanced
Find the equation of the tangent line to \(f(x)=x^{2}\ln(x)\) at \(x=1\).
Choose one option.
Show answer
- C. \( y = x - 1 \)
Explanation
Compute \(f(1)=0\) and, by the product rule, \(f'(x)=2x\ln(x)+x\), so \(f'(1)=1\). The line is \(y=x-1\).
Review the concept: Tangent line
The tangent line to the graph of \(f\) at the point \((a,f(a))\) is the line through that point with slope \(f^{\prime}(a)\). It is the best linear approximation of \(f\) near \(a\).
\[y-f(a)=f'(a)\,(x-a)\]
More practice problems: tangent line
- ZW-TANGENT-LINE-001 Find the equation of the tangent line to f(x)=x^2 at x=1.
- ZW-TANGENT-LINE-002 Find the equation of the tangent line to f(x)=x^3 - 2 x at x=2.
- ZW-TANGENT-LINE-003 Find the equation of the tangent line to f(x)=√x at x=4.
- ZW-TANGENT-LINE-004 Find the equation of the tangent line to f(x)=(1)/(x) at x=1.
- ZW-TANGENT-LINE-005 Find the equation of the tangent line to f(x)=e^x at x=0.
- ZW-TANGENT-LINE-006 Find the equation of the tangent line to f(x)=ln (x ) at x=1.
- ZW-TANGENT-LINE-007 What is the slope of the tangent line to f at x=a?
- ZW-TANGENT-LINE-008 Through which point must the tangent line to f at x=a pass?