Page 151 - How To Solve Word Problems In Calculus

We differentiate to find the critical numbers.

2 1

t (θ) =− sin θ +
3 3
2 1
0 =− sin θ +
3 3
2 1
sin θ =
3 3
1
sin θ =
2

π
θ =
6

2 θ
Since t(θ) = cos θ + is a continuous function of θ, the ab-
3 3
solute minimum may occur at the critical number or at an
endpoint of the interval [0,π/2].

2
t(0) = ≈ 0.667
3
√ √

π 2 3 π 6 3 + π
t = · + = ≈ 0.752
6 3 2 18 18

π π
t = ≈ 0.524 ←absolute minimum
2 6

To minimize the time to get from A to B, the man should jog
completely around the lake.

EXAMPLE 7
Two vehicles, A and B, start at point P and travel east at rates
of 10 km/h and 30 km/h, respectively. An observer at Q,1km
north of P, is able to observe both vehicles. What is the max-
imum angle of sight between the observer’s view of A and B?

138