Find the linearization of \sqrt{x} at x = 4 i.e, find a linear approximation of \sqrt{x} for x close to 4. i.e, find equation of tangent line to \sqrt{x} at x = 4.

Approximate \sqrt{5} Method 1: Use equation of tangent line

Method 2 (even easier): Use Δy ∼ dy Recall: slope of secant line = \frac{Δy}{Δx} Δx = x+h−x, Δy = f(x+h)−f(x) = f(x+Δx)−f(x) slope of tangent line = f′(x) = \frac{dy}{dx}. Thus dy = f′(x)dx. If Δx = dx, then Δy ∼ dy f(x + Δx) = f(x) + Δy ∼ f(x) + dy