How do I get fxx, fyy, and fxy?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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How do I get fxx, fyy, and fxy?
Review: Find and classify CPs of
f(x,y) = ex² + y² - 2x
fx = (2x-2) ex²+y = xx sex
= 0
X=1
1
*e any # > 0
fy=(zy) ex+y = 2x = 0, y = 0
⇒ CP = (1,0)
ze"
fxx= ₂ex²+y²= 2x + (2x-2) ² ex-y-2x
fyy= ₂₁x²= y ²-³x + 4y²ex=y²-xx
+ 2x
20
fxy= 2y (2x-2) ex²+y²-2x
0
H(1,0) = 26" (ze")-0² >
fxx (₁₁0) = 2e²¹ > 0
→ Relative Min at (1,0)
#
Transcribed Image Text:Review: Find and classify CPs of f(x,y) = ex² + y² - 2x fx = (2x-2) ex²+y = xx sex = 0 X=1 1 *e any # > 0 fy=(zy) ex+y = 2x = 0, y = 0 ⇒ CP = (1,0) ze" fxx= ₂ex²+y²= 2x + (2x-2) ² ex-y-2x fyy= ₂₁x²= y ²-³x + 4y²ex=y²-xx + 2x 20 fxy= 2y (2x-2) ex²+y²-2x 0 H(1,0) = 26" (ze")-0² > fxx (₁₁0) = 2e²¹ > 0 → Relative Min at (1,0) #
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