3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have critical points at (0, 4) and (2, 0).

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

A:

Q: Find the coordinates of a fourth point so that the four points form the vertices of a rectangle. 64…

A: We have to find the coordinates of the fourth vertex to make it a rectangle.

Q: The curve crosses the x axis at A(2, 0) and at the point B(10, 0). The curve has a minimum at M(3,…

A:

Q: Find the tangent line to the ellipse 0y-x-8 0,-1,-√7 y = 14 0y=-√14x-7 O None of these ○ y = √7x-8 1…

A:

Q: Find the orthogonal trajectories of the family of curves y = ax² + 4ax + 4a, where a being…

A: Orthogonal trajectory: If a curve cuts every member of a given family of curves at right angle, then…

Q: Q3) Determine slope of a curve y = x + 2 at p(1,3) and q(3,11)

A: Slope of a curve : The slope of a curve y=f(x) at a point P is the slope of the tangent at that…

Q: 4) Find the orthogonal trajectories of the family of curves

A:

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: Arc length is defined as the distance between two points on the curve. It is done in such as way…

Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

A:

Q: show solution to #33 of the attached

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Find the equation of the place that pusses + through the point= (-1,2,1) Contains the line of…

A:

Q: 0. F A particie moves along a norizontal line. Its position function is s(t) problem, find the…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: If y=f(x) be the curve that lies on the xy plane, then its length from x=a to x=b is given by…

Q: If A = 3a_0 + 2a_0 - 5a_z and B = -2a_p + 3a_0- a_z are given at points P(3,T1/6,5) and Q(4,T1/3,3)…

A:

Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

A:

Q: IT Find the orthogonal trajectories to the given curve -3x y= 3x-1 + Ce C

A: With the help of derivative with respect to x and changes (dy)/(dx) by -(dx)/(dy) Then we find the…

Q: Analytically determine the highest point on the curve of intersection of x² + y² + z² 2x+y=z=2.…

A: