Chapter 1.1, Problem 59E

2. Find the Bezier surface equation using the 9 control points shown below. Use the u and v directions shown. It is required to show all the calculation processes for finding Bernstein polynomials. Find the surface tangent, twist and normal vectors at point u=0.5 and v=0.5. (40 points) y 10 9 8 7 6 5 4 3 2 Poo и 1 1 2 3 4 5 6 7 8 9 10 10 X

A cable runs along the wall from C to P at a cost of $24 per meter, and straight from P to M at a cost of $26 per meter. If M is 10 meters from the nearest point A on the wall where P lies, and A is 72 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost. C 72 P A 10 M

The number of bank robberies in a country for the years 2010-2018 is given in the following figure. Consider the closed interval [2010,2018]. (a) Give all relative maxima and minima and when they occur on the interval. (b) Give the absolute maxima and minima and when they occur on the interval. Incidents 7000- 6000-5 5482 5000- 4424 4273 4822 4000- 3708 3748 4229 4089 3000- 2582 2000- 1000- 0 2010 2012 2014 2016 2018 Year