Recall that the volume of a sphere of radius r is V(r) =4\, \pi\, r^3 /3.

Question

Find L, the linearisation of V(r) at r=50

Answer 1

v = 4π/3 r^3
v' = 4π r^2
at r=50, v = 500π/3 and v' = 100π

So, the tangent line at r=50 is

v - 500π/3 = 100π(x-50)