Answer to Question #262712 in Calculus for Alunsina

Question

Given the function y=√x

a. Find the differential dy.

b. Evaluate dy and ∆y if x=1 and dx=∆x=1

c. Find the equation of the tangent line at x=1

d. Sketcg the graph of the curve y=√x and the tangent line in the Cartesian Plane using a scale of 1 unit = 1cm. Show in your diagran the line segments dx, dy, and ∆y. (Note: the curve us an upper semi-parabola whose vertex is at the origun and concaving to the right. Use 0, 1, 4, and 9 as x-coordinates.)