A Particle Is Traveling Along a Helix Whose Vector Equation $\mathbf { r } ( t ) = \left\langle R _ { 1 } \cos \alpha t , R _ { 2 } \sin \alpha t , \beta t \right\rangle$

Essay

A particle is traveling along a helix whose vector equation is given by $\mathbf { r } ( t ) = \left\langle R _ { 1 } \cos \alpha t , R _ { 2 } \sin \alpha t , \beta t \right\rangle$ , where $R _ { 1 } \geq R _ { 2 }$ . Find its maximum and minimum speeds.