Find the Bézier curve (x(t),y(t)) through the points (1,0) and (3,0) with control points (1,2) and (3,2). (1+ 6t² – 4t³, 6t – 6t²) (1+ 2t – 3t2 + t³, 2t – 3t² +t³) O (1+4t² – 2t³, 6t – 6t³ ) (1+ 6t² – 4t³, 3t – 3t2)
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- Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition. Make the curve y= ax^3+bx^2+cx+d have critical points (1,0) and (-2,27)find absolute maximum and minimum of f(x,y)=x^3+3xy-3y^2+2 in a region whose vertices at (-1,-1) (-1,1) (1,1) (1,-1)Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular region whose vertices are (0,0), (6,0), and (0,4).
- Find the absolute maximum and minimum values of f(x, y) = 3xy−6x−3y + 7 on the closed triangular region R with vertices (0, 0), (3, 0), and (0, 5).Let u(x,y) satisfy the following equationuxx+(x2+y2-1)uyy=0Find the region in which the equation is elliptic and the region in which the equation is hyperbolic.Find the point on the plane x+5y+2z=14 closest to the point (1,1,1).
- Find the absolute maximum and minimum values of f(x, y) = 4xy^2 − x^2y^2 − xy^3 on the closed triangular region in the xy-plane with vertices (0, 0), (0, 6), and (6, 0).Find the equilibria of x_(t+1)=0.9x_(t) when t= 0, 1, 2, 3 ... and use cobbwebing to determine the stability of the equilibria.Find the absolute maximum and minimum of f(x,y)= 4xy^2 - (x^2)(y^2) - xy^3 on the closedtriangular region with vertices (0,0), (0,6), and (6,0).
- Find the minimum distance from the point (−2, −2, 0) to the surface z = √(1 − 2x − 2y).Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).Find the maximum and minimum values of ƒ(x,y,z)=x^2+y^2+z^2 on the curve on which the cone z^2 = 4x^2 + 4y^2 and the plane 2x+4z=5 intersect.