Lv 1- wu-uv-JJ Question 4. In class we showed that if f (t) is a vector function that lies in a sphere {9' st. lfr'l = r}, then t) J. f'(t) fer all t. Now we will show the converse: if t) J. f'[t) for all t, then f lies in a sphere. 4.1. Express (f - f}'(t) in terms of (f- f')(t). [1 point] 4.2. Assume t) J. f'(t). Show that there is some real number 1" such that |f(t)| = r for all t. Hint: Show that the function ( f - f)(t} = | f (t)|2 is constant by considering its derivative. Since |f(t]| is always nonnegative, it will follow that |f(t)| = 4.! [f - f)(t) is also constant. I"! nni H+Gl|