Make the curve y = ax4 + bx³ + cx² + dx + e pass through the point (1, -8) be tangent to the line y= 11x - 5 at (1, 6) and have a critical point at (0, 3). Show step-by-step solution.
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A: We will find the value of a, b, c, and d as following .
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A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems
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A: we have to determine a,b,c and d so that the curve y=ax3+bx2+cx+d will have a critical point at…
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A: Answer
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A: Since you have asked multiple questions, as per our policy we will answer first question. Please…
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A: Please see the below picture for detailed solution.
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A: Note: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should…
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A: I am attaching image so that you understand each and every step.
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- Determine a,b,c and d so that the curve y=ax^3 + bx^2 + cx + d will have a critical point at (0,-2) and also tangent to the line 3x+y+3=0 at (-1,0)A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y) is T(x, y) = 10 − x^2 − y^2. Find the path of the particle as it continuously moves in the direction of maximum temperature increase.Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c
- Find the first partial derivative wx, wy, and wz of (x + yw )2 – ez – 2 = 0 Make the solution detailed and clear. Please write it in a paper.Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that passes through thegiven point. y' = y - 2x , (1,0)
- The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How is the behavior of the two functions at the critical point different?Use partial derivatives to find the coordinates which give the shortest distance from the point (2,0,0) to the plane 3x+2y-z=2. Confirm that the point is the shortest distance with use of second derivativesRevolve about the line x= -1, use disk method. (Bound by y=x4, x=0, and y=16. Mark axis of rotation, draw appropriate differential elements on a graph, and lable all the appropriate dimensions and features.)
- Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line x-1=0. with complete solutionA ball is thrown upward from the top of a 200-foot tall building with a velocity of 40 feet per second. Take the positive direction upward and the origin of the coordinate system at ground level. What is the initial value problem for the position, x(t), of the ball at time t?Demonstrate the use of the method with reflections on the use of numerical methods, find the minimum for the function below: F(x,y)= Ax^2 - Bxy- cy^2= x -y (Xo=4, Yo=4) A=2 B=-2 C=1 Identify the minimum again using the Newton’s method with dynamic . However, use this time numerical derivatives instead of . When using numerical derivatives, only one of the constants is being varied as with partial derivatives. Apply in this case the forward numerical derivative, . Here equals some very small number. For each step , solve first the and optimal using the condition . When taking the derivative of , please remember to consider the inner derivatives for each of the coordinate axes that results as dot product with the main function. In this work it is enough that only the second term in the dot product is analyzed using numerical derivatives. Thus, the function takes the form .