Exercise · ZW-TANGENT-LINE-002 · ★★☆ Intermediate
Find the equation of the tangent line to \(f(x)=x^{3} - 2 x\) at \(x=2\).
Choose one option.
Show answer
- B. \(y = 10 x - 16\)
Explanation
Compute \(f(2)=4\) and \(f'(x)=3 x^{2} - 2\), so \(f'(2)=10\). The line is \(y-f(2)=f'(2)(x-2)\), that is, \(y = 10 x - 16\).
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-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?
- ZW-TANGENT-LINE-009 Find the equation of the tangent line to f(x)=x^2ln (x) at x=1.