This is MULTIVARIATE Calculus question. PLEASE DO NOT PROVIDE text book extracts – NOT acceptable. No standard solutions acceptable either. Any solution has to address the question exactly.
If you do not have any MULTIVARIATE calculus background- DO not waste your time – with political science degree background. Thank you.- see attached file for further clarity.
1.Consider the function
f(x,y)=f(x,y) =x^3/3 −yx^2/2 −αx^2/2+ αyx +2y^3/3+ y^2
where α ≥ 0 is an unspeciﬁed coeﬃcient. There are two values of α for which f(x,y) has three distinct critical points. The ﬁrst of these is α = 0, where the critical points of f(x,y) are (0,0), (0,−1) and(-4/3,-4/3) . The second we will denote α∗.1
a) Determine the value of α∗ > 0 for which f will have three distinct critical points.
b) Use the second derivative test to characterize the critical points of f when α = 0.
2. Use the method of Lagrange multipliers to determine the minimum value of
f(x,y,z) =x^2+y^2+z^2 subject to the constraints
x + 2z = 6 and x + y = 12
State the minimum value of f and the associated values of x, y and z.
Looking for solution of this Assignment?
WHY CHOOSE US?
We deliver quality original papers |
Our experts write quality original papers using academic databases. |
Free revisions |
We offer our clients multiple free revisions just to ensure you get what you want. |
Discounted prices |
All our prices are discounted which makes it affordable to you. Use code FIRST15 to get your discount |
100% originality |
We deliver papers that are written from scratch to deliver 100% originality. Our papers are free from plagiarism and NO similarity |
On-time delivery |
We will deliver your paper on time even on short notice or short deadline, overnight essay or even an urgent essay |