
Maxima and Minima 7-21
∴ = ≅x 10 3 17 32. .
We also see that q′ is +ve for x < 17.32 and q′ is -ve for x > 17.32.
Thus, q′(x) changes its sign from positive to negative as x passes through 17.32. Hence, q must be
maximum at x = 17.32.
Therefore, the distance at which one should sit from the wall so that the viewing angle of the image is
maximum is 17.32 ft.
Also the largest viewing angle
θ =
−
=
( )
−
− −
−
tan tan
tan t
1 1
1
30
10 3
10
10 3
3 aan
.
−
= − =
1
1
3
3 6 6
π π π
Example 7.16 A farmer needs to fence a rectangular field that borders a high-way road on one of its
sides. He has 1000 ft of fencing material available and ...