Find the value of a so that the work done by the force ♬ = (y² + 1)² + (z+y) in moving from (0,0) to (1,0) along the curve y = az(1-2) is a minimum. At α = ☐ where W min = [ Fractions please:)
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- Find r’(t), r(t), and r’(t) for the given value of tå. r' (t) r(to) r'(to) = = = = r(t) = 3 cos(t)i + 3 sin(t)j, to T 2 Sketch the curve represented by the vector-valued function and sketch the vectors r(t) and r'(t). = r(t) starts at (x, y) = (0, 0) and ends at (x, y) = r'(to) starts at the terminal point of r(t) at (x, y) = and ends at (x, y) =2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the vector v (1,2) at the point (0,-2). b) Find a unit vector u in the direction in which f decreases most rapidly at the point (0,-2).