Two small arches have the shape of parabolas. The first is given by x) = 1

Two small arches have the shape of parabolas. The first is given by ƒ x) = 1 − x² for −1 ≤ x ≤ 1 and the second by g(x) = 4 − (x − 4)² for 2 ≤ x ≤ 6. A board is placed on top of these arches so it rests on both (Figure 20). What is the slope of the board? Find the tangent line to y = ƒ(x) that intersects y = g(x) in exactly one point.