The curve C in the x-y plane is given parametrically by ( x ( t ) , y ( t ) ) , where d x d t = t sin ( 2 t 3 ) and d y d t = cos ( t 2 4 ) for 1 ≤ t ≤ 6 . a. Find the slope of the line tangent to the curve C at the point where t = 3 . b. For 1 ≤ t ≤ 6 , what is the value of t at which the line tangent to the curve C is vertical? c. Find the length of the curve C for 1 ≤ t ≤ 6 .