Optimization A. A farmer plans to fence a rectangular pasture adjacent to a river (see figure). The pasture must contain 245,000 square feet in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river? B. point (x,y) in the first quadrant along the curve y = V9 7 x that maximizes area of rectangle where the origin (0,0) and (x,y) are at opposite ends of one diagonal (ire. Aim) = xv) C. point on curve y : 10 x/S at minimum distance from the point (3,2) Differentials A. Find the differential Find dy, where y = 3Vx2 + 2 Find dy, where y = 9'5 B. Use the differential to compute dy and compare with y. y: x4+1atx=-2; Ax=dx= 0.05 C. (applied) D. Linearization of Function about a Point (equivalent to tangent line) Find the linearization of the function f(x) = V13 + 1 around the point at x=2. Chapter 5 Integrals; Fundamental Theorem of Calculus Velocity and Position Free fall: An object is thrown upward from a height of 123 feet with an initial velocity of 32 ft/sec upward. Find the position function r(t) if the only force is that of gravity, a(t) = -32feet/sec1. Displacement and Distance Travelled Suppose an object is moving with velocity given by v(t). Find both the displacement and the distance travelled over the given interval [a,b]. a) v(t) = 8 2t on [0,5] b) v(t) = t2 t Z on [1,4]