13. The mechanical power output P in a contracting muscle is given by:

where T is the muscle tension, v is the shortening velocity (max of ), is the isometric tension (i.e., tension at zero velocity), and k is a nondimensional constant that ranges between 0.15 and 0.25 for most muscles. The equation can be written in nondimensional form:

where , and . Consider the case .

(a) Plot p versus u for .

(b) Use differentiation to find the value of u where p is maximum.

(c) Find the maximum value of p.