Find the linearization L (x, y) of the function f (x, y) = y/-x at (-9, 4).

(part 1 of 4) A function f is defined by f(x, y) = (x+8) (y-6)(x + y − 4). - (i) Determine fx for the function f. 1. fx(x,y) (x + 8) (x - 2y + 4) 2. fz(x, y) 3. fx(x,y) 4. f(x,y) 5. fx(x, y) 1. fy(x, y) 2. fy(x, y) = 3. fy(x, y) - = = = (part 2 of 4) (ii) Determine fy for the function f. = = = (y + 8) (2x + y +12) (x − 6) (x + 2y — 10) = (y − 6)(2x − y + 12) (y − 6) (2x + y + 4) (y − 6) (2x + y − 10) (y +6)(2x + y + 4) (x + 8) (x + 2y — 10) - 4. fy(x, y) = (x + 8) (x + 2y + 2) 5. fy(x, y) (x − 6) (x – 2y — 10)

Q4) Find the linearization of: f(x) = x³ + 10 when a = -3

Q2/ A/ plot the function Z= 3(1-x) e-x²-(v+1)² – 10(x – x³ – y5)e-x²-y² _ ! e-(x+1)²-y² where -35xS3, -35ys3.

Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 = (x - 1)(x+1)2. 4.

Estimate of f′(3)

The Linear approximation (linearization) of f(x) = √ at x = 27 is (A) y = 3+27(x - 27) (B) y = 3+ (x - 27) (C) y = 27+7(x-27) (x − 3) (D) y = 3 + (E) y = 3+ (x - 27)

X S(x) 9 I A) f(x)=2x-3 B) f(x)=-2x+3 C) f(x)=2x-1 D) f(x)=-2x+1 www BIHORE 1 The table above shows some values of the linear function. Which of the following defines f?

Determine which of the following pairs of functions are linearly independent. NO_ANSWER v 1. f(0) = cos(30) g(0) = 16 cos (0) – 12 cos(0) NO_ANSWER v 2. f(t) = 4t² + 28t g(t) = 4t2 – 28t

Let f(a, y) = 3x² + 4y2 – axy. (a) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive x-direction. (b) Find the values of a such that the graph of f increases when moving from the point (1, 2) in the positive y-direction.