Suppose that f(x, y, z) = (1+x + y² + z³)4 + ln (1 + 3x + 2y + z).

Linear Algebra: A Modern Introduction
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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• Problem. Suppose that f(x, y, z) = (1 +x + y² + z³)4 + ln (1+ 3 + 2y + 2).
A. Find the differential
af
af
Əy (2, Y, z) Ay +
(x, y, z) Az
dz
df (x, y, z)
(x, y, z) Ax +
of this function at (x, y, z) = (0,0,0).
B. Use the Linear Approximation Formula
f (x + Ax, y + Ay, z + Az) × f(x, y, z) + df (x, y, z)
and your answer in part A to estimate f(-0.1,0.2,0.1).
C. Evaluate f(-0.1,0.2,0.1) with five decimal places using your calculator and compare that value
with your answer in part B. Is the linear approximation an under, or an over estimate of the actual
function value?
Transcribed Image Text:• Problem. Suppose that f(x, y, z) = (1 +x + y² + z³)4 + ln (1+ 3 + 2y + 2). A. Find the differential af af Əy (2, Y, z) Ay + (x, y, z) Az dz df (x, y, z) (x, y, z) Ax + of this function at (x, y, z) = (0,0,0). B. Use the Linear Approximation Formula f (x + Ax, y + Ay, z + Az) × f(x, y, z) + df (x, y, z) and your answer in part A to estimate f(-0.1,0.2,0.1). C. Evaluate f(-0.1,0.2,0.1) with five decimal places using your calculator and compare that value with your answer in part B. Is the linear approximation an under, or an over estimate of the actual function value?
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