If You Were to Drag a 200 Pound Object Along $F ( \theta ) = \frac { 200 k } { \cos \theta + k \sin \theta }$

Essay

If you were to drag a 200 pound object along a horizontal surface, then the smallest force F that is necessary to drag that object is given by $F ( \theta ) = \frac { 200 k } { \cos \theta + k \sin \theta }$ where $\theta$ is the angle (in radians) your arm makes with the ground and k > 0 is the coefficient of friction for the surface. Find a formula for $F ^ { \prime } ( \theta ) \text { for } 0 \leq \theta \leq \frac { \pi } { 2 }$