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Equation of a Tangent Line: Problems and Solutions

Equation of a Tangent Line or Normal Line: Problems and Solutions

Are you working to find the equation of a tangent line (or normal line) in Calculus? Let’s solve some common problems step-by-step so you can learn to solve them routinely for yourself.

CALCULUS SUMMARY: Tangent & Normal Lines
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Tangent/Normal Line Problem #1
For a particular function $g$, we know $g'(5) = 2$ and $g(5) = -3$. Write an equation for the line tangent to $g$ at $x = 5$.
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Tangent/Normal Line Problem #2
Consider the curve given by $y = f(x) = x^3 – x + 5$.
(a) Find the equation to the line tangent to the curve at the point (1, 5).
(b) Find the equation of the line normal (perpendicular) to the curve at the point (1, 5).
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