Practice Tangent Line in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A line that touches a curve at exactly one point and has the same slope as the curve there.
The tangent line is the unique straight line that best approximates the curve at a specific point — same value, same slope.
Example 1
easyFind the equation of the tangent line to f(x) = x^2 + 3 at x = 2.
Example 2
mediumFind the equation of the tangent line to g(x) = \sqrt{x} at x = 9, and use it to approximate \sqrt{9.1}.
Example 3
easyFind the equation of the tangent line to h(x) = 3x^3 - x at x = 1.
Example 4
hardAt what point(s) on f(x) = x^3 - 3x does the tangent line have slope 9?