answer in radian mode for all the questions
3. Find the equation of the tangent to the curve y = cos2 2 when = Round final answers to two decimal places. [4 marks]
4. Find the equation of the tangent line to the curve y = e" when it is parallel to 2x-y= 5.[4 marks]
5. Find the intervals of increase and decrease for the function f() = 3e [4 marks]
6. Find the minimum value(s) of the function f() = e --2. [4 marks]
7. Determine the maximum and minimum point(s) for y=sin(2x) + 3cos(x) + x on the interval 0<x< 2T. [4 marks]
8. A child is flying a kite attached to a 20 m long string. At first, the kite is directly above the child, but it blows east. The child notices that the angle between the string and the ground is decreasing by 5' each second. How quickly is the kite moving horizontally when the angle between the string and the ground is 76'? [6 marks]
9. The position of a particle as it moves horizontally is described by the model s = sin t cos t on the interval 0 < t < 2. If s is the displacement in
metres and t is the time in seconds, find the maximum and minimum
displacements and when they occur. [4 marks]
10. An artist has 9 m of wire. They will cut it into two pieces. One will be bent into a
square while the other will be bent into a circle. Where on the wire should they cut to get the smallest total area? [6 marks]
