Let us imagine the line BC is straight, even if it ios not in the drawing.

So R(x) has two branches that are continuous at B.

The parabolic branch AB is

R(x) = ax^2

At B, it is (1000,100), so,

100 = a(1000)^2

a = 100 /(1000)^2

a = 10^(-4) = 0.0001

Hence,

R(x) = (0.0001)x^2

The tangent line at B has the slopes:

--R'(x) = 2ax for the parabola, and,

--R'(x) = b for the straight line.

Since R'(x) = R'(x) at B, thenn

b = 2ax

b = 2(0.0001)(1000)

b = 0.2 ----------------------answer.