Tangent Line to a Square Root Curve

The point is (4, √4) = (4, 2). The derivative is y′ = 1/(2√x), which is 1/4 at x = 4. Point-slope form: y − 2 = (1/4)(x − 4), so y = x/4 + 1. Check: 4/4 + 1 = 2. TI-36X Pro tip: press 2nd, d/dx, enter √(x) in the first box, move right to the last box, enter 4, and press enter. The slope is 0.25, matching 1/4.