Find the slope-intercept equation of the normal line to a curve involving a square root at a given point.

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Equation of a Normal Line Using the Chain Rule

The chain rule warmup

Find the slope-intercept equation of the normal line to the curve \(y = \sqrt{x^2+16}\) at the point \((3,5)\).

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What you need first

the chain rule
the power rule for derivatives
the relationship between the slopes of perpendicular lines
point-slope form of a linear equation
slope-intercept form of a linear equation

What this problem tests

Tests the ability to apply the chain rule, evaluate a derivative at a point, find the slope of a normal line, and write the equation of a line in slope-intercept form.

This is a standard introductory calculus problem testing the application of the chain rule to find geometric properties of curves.

Equation of a Normal Line Using the Chain Rule

What you need first

What this problem tests

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