The mechanical power output Pin a contracting muscle is given by:

where T is the muscle tension, v is the shortening velocity (max of vmax), T0 is the isometric tension (i.e., tension at zero velocity), and k is a non-dimensional constant that ranges between 0.15 and 0.25 for most muscles. The equation can be written in non-dimensional form:

where p = (Tv)/(T0vmax), and u = v/vmax. Consider the case k = 0.25.
(a) Plot p versus u for 0 (b) Use differentiation to find the value of u where p is maximum.
(c) Find the maximum value of p.

m() TV p-n- ku(1 u)