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Let y=p(x) betheimplicit function corresponding to the equation f(x, y) = log(9) and such that p(3) = –1. Compute the function y = 4(x) explicitly, find its definition domain and compute its derivative '(x). Check that the %3D formula: oʻ (x) = %3D af dy , (x, 9(x)) holds.

Let y=p(x) betheimplicit function corresponding to the equation f(x, y) = log(9) and such that p(3) = –1. Compute the function y = 4(x) explicitly, find its definition domain and compute its derivative '(x). Check that the %3D formula: oʻ (x) = %3D af dy , (x, 9(x)) holds.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve the d part only. Thank you
Problem 2 f(x, y) = log(x² – y² + 1) (a) Find the definition domain D of z=f(x,y) and draw it in thexy plane. (b) Computethe partial derivatives and the Hessian matrix of z=f(x,y) at each point (x, y) € D. (c) Find the local maxima, the local minima and thesaddle points of the function z = f(x,y). (d) Let y=p(x) be theimplicit function corresponding to theequation f (x, y) = log(9) and such that p(3) = –1. Compute the function y = its definition domain and compute its derivative '(x). Check that the formula: p(x) explicitly, find af E (x, p(x)) oʻ (x) = af holds. (e) Prove that the line whose equation is 2y=x+1 is included in D and draw it in the xy plane. Find the maxima and the minima of z=f(x,y) under the condition x – 2y +1 = 0. (f) Let C betheset of points (x,y)satisfying the equation x² + 4y? = 1. 4 Prove that C is an ellipse which is included in D and draw it in the xy plane. Find the maxima and the minima of z = f(x, y) under the condition x² + 16y? – 4 = 0.
Transcribed Image Text:Problem 2 f(x, y) = log(x² – y² + 1) (a) Find the definition domain D of z=f(x,y) and draw it in thexy plane. (b) Computethe partial derivatives and the Hessian matrix of z=f(x,y) at each point (x, y) € D. (c) Find the local maxima, the local minima and thesaddle points of the function z = f(x,y). (d) Let y=p(x) be theimplicit function corresponding to theequation f (x, y) = log(9) and such that p(3) = –1. Compute the function y = its definition domain and compute its derivative '(x). Check that the formula: p(x) explicitly, find af E (x, p(x)) oʻ (x) = af holds. (e) Prove that the line whose equation is 2y=x+1 is included in D and draw it in the xy plane. Find the maxima and the minima of z=f(x,y) under the condition x – 2y +1 = 0. (f) Let C betheset of points (x,y)satisfying the equation x² + 4y? = 1. 4 Prove that C is an ellipse which is included in D and draw it in the xy plane. Find the maxima and the minima of z = f(x, y) under the condition x² + 16y? – 4 = 0.
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