When blood flows along a blood vessel, the ux F is proportional to the fourth power of the radius R of the blood vessel: F = '93\" , where k is a constant A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inated inside the artery in order to widen it and restore the normal blood ow. Suppose a patient with a partially clogged artery has R = 2 before surgery. (a) Find the equation of the tangent line of F at R = 2. (b) Suppose the surgery increased R by 20% so that the ux F is increased accordingly. Use the tangent line in Part {al to approximate the value of F after the surgery. (c) Mthout computing the actual value of F after the surgery, estimate the error in the approximation in Part lb} (d) Use the actual value of F after the surgery to compute the actual value of the error in the approximation in Part (b). (Hint: Your answer to all 4 parts should have the constant k in it. Do not round and keep all decimal places in your calculation - there should be no more than 4 decimal places.)