Determine the Critical points and its classification 6. Determine a, b, c and d so that the curve y = ax3 + bx2 + cx + d so that the curve will havea critical point at (0, -2) and also tangent to the line 3x + y + 3 = 0 at (-1, 0).7. Make the curve y = axª + bx³ + cx² + dx + have a critical point at (0, 3) and have aninflection point at (1, 2) with inflectional tangent 6x + y = 8.8. Determine a, b, c and d so that the curve y = ax³ + bx² + cx + dpass through (-1, -1) andhave at (1, 3) an inflection point with inflectional tangent 4x − y = 1.9. Find a cubic function y = ax³ + bx² +cx+d that has a local maximum value of 3 at -2 anda local minimum value of 0 at 1.10. Find a cubic function y = ax³ + bx² + cx+d that has a local maximum at (4, 0) and passthrough (1, -1).

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Answered: 6. Determine a, b, c and d so that the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The curve ax4+bx3+cx2+dx+k passes thru P1 (5, –210), has a critical point at P2 (4, –416), and an inflection point at P3 (2, 0) where a,b,c,d,k are non zero constants. 1. What are the values of a,b,c,d,k? 2. What type of critical point is P2?
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)
Show that (0, 0) is a critical point of ƒ(x, y) = x2 + kxy + y2 no matter what value the constant k has.
Find the critical points of the curve: y=1/3 x^3 -1/2 x^2-2x+2 and specify what kind of points are it.
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?
The functions f (x, y) = x^2 + y^2 and g(x, y) = x^2 − y^2 both have a critical point at (0, 0). How is the behavior of the two functions at the critical point different?
Find the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x >0, y>0) and show that ƒ takes on a minimum there.
Consider a firm whose revenue is expressed through the function R(x,y)= 4x³y², where x and y represent the quantities of two goods produced. Suppose these quantities depend on capital k and labor in addition to good y still depend on the availability of material m. This occurs according to the functions x= 4k+ 3L and y = 3k + L+m. Calculate the partial derivatives of income in relation to capital, labor and availability as functions of such variables
Show that f(x, y) = x^2 + y^2 − 2xy + 4 has infinite number of critical points and that D = 0 at each one. Then show that f has a local (and absolute) minimum at each critical point.
Let y be the solution of the initial value problemy" +y = - sin(2x), y (0) = 0, y'(0) = 0.The maximum value of y is
construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. 1.dxdt=−x3+xy2,dydt=−2x2y−y3; asymptotically stable
Obtain the particular solution satisfying the initial conditions indicated.

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6. Determine a, b, c and d so that the curve y = ax3 + bx2 + cx + d so that the curve will have a critical point at (0, -2) and also tangent to the line 3x + y + 3 = 0 at (-1, 0). 4 hy3 ar² dr La