What is the percent change in g when moving from sea level

Question

Question: The acceleration due to gravity, g, is given by

g = GM/r²,

where M is the mass of the earth, r is the distance from the center of the earth, and G is the universal gravitational constant.

(a) Show that when r changes by Δr, the change in the acceleration due to gravity, Δg, is given by

Δg ≈ -2g(Δr/r)

(b) What is the significance of the negative sign?

(c) What is the percent change in g when moving from sea level to the top of Pike's Peak (4.315 km)? Assume the radius of the earth is 6400 km.