Tangent line to a linear plus a radical at a given point: Find the equation of the tangent line to

at the point .

First we need to find the slope at any point, i. e. the derivative:

.

At the slope is .

Consequently, the tangent line must have this slope, and in slope-intercept form:

Since this line goes through the given point, , we can use its coordinates in this equation to determine

the y-intercept, b:

, or

We can combine these results to get the equation of the tangent line as