Two hallways, one of
width 3 feet, the other of width 4 feet, meet at a right angle.
See the illustration below.

(a) Express the length L of the line segment shown as a
function of the angle (-).

(b) Discuss why the length of the longest ladder that can be
carried around the corner is equal to the smallest value of L.

Is there a direction u in which the rate of change of f(x,y)equals=x squared minus 3 xy plus 4 y squaredx2−3xy+4y2 at p(1,2) equals 14? give reasons for your answer. choose the correct answer below. a. no. the given rate of change is smaller than the minimum rate of change. b. no. the given rate of change is larger than the maximum rate of change. c. yes. the given rate of change is larger than the minimum rate of change and smaller than the maximum rate of change.