Figure 2 shows the curve

Cwith equation $\displaystyle y = 3x-4\sqrt{x} + 2 $ and the tangent toCat the pointA.

Given thatAhasx-coordinate 4,

(a)show that the tangent toCatAhas the equationy= 2x -2.

The shaded region is bounded by

C, the tangent toCatAand the positive

coordinate axes.

(b)Find the area of the shaded region.