f(x,y) = x^2+ y^2 - 2x + 2y + 5 Step 1: Locate all critical points) Step 2: Calculate the determinants and classity the critical point (s) (local max, local minimum or saddle) (Please show your calculations for second derivatives.) Step 3: Find the relative maximum and/or minimum of f(x, y) Step 4: Find the maximum and minimum values of f(x,y) on the set D = (x, y) : x^2+ y^2 ≤4 4] (the closed disk centered at (0, 0) with radius 2). Hint: Let x = 2cos (0) and y = 2sin (0), then rewrite f(x, y) as f(0).
f(x,y) = x^2+ y^2 - 2x + 2y + 5 Step 1: Locate all critical points) Step 2: Calculate the determinants and classity the critical point (s) (local max, local minimum or saddle) (Please show your calculations for second derivatives.) Step 3: Find the relative maximum and/or minimum of f(x, y) Step 4: Find the maximum and minimum values of f(x,y) on the set D = (x, y) : x^2+ y^2 ≤4 4] (the closed disk centered at (0, 0) with radius 2). Hint: Let x = 2cos (0) and y = 2sin (0), then rewrite f(x, y) as f(0).
f(x,y) = x^2+ y^2 - 2x + 2y + 5 Step 1: Locate all critical points) Step 2: Calculate the determinants and classity the critical point (s) (local max, local minimum or saddle) (Please show your calculations for second derivatives.) Step 3: Find the relative maximum and/or minimum of f(x, y) Step 4: Find the maximum and minimum values of f(x,y) on the set D = (x, y) : x^2+ y^2 ≤4 4] (the closed disk centered at (0, 0) with radius 2). Hint: Let x = 2cos (0) and y = 2sin (0), then rewrite f(x, y) as f(0).
f(x,y) = x^2+ y^2 - 2x + 2y + 5
Step 1: Locate all critical points)
Step 2: Calculate the determinants and classity the critical point (s) (local max, local minimum or
saddle) (Please show your calculations for second derivatives.)
Step 3: Find the relative maximum and/or minimum of f(x, y)
Step 4: Find the maximum and minimum values of f(x,y) on the set D = (x, y) : x^2+ y^2 ≤4
4] (the closed disk centered at (0, 0) with radius 2).
Hint: Let x = 2cos (0) and y = 2sin (0), then rewrite f(x, y) as f(0).
Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
