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3 years ago

Q4.A/Find the linearization L(x, y) of the function f(x, y) = (x + y + 2)² at p. = (1,2)

Mathematics

1 answer:

Dafna11 [192]3 years ago

3 0

Answer:

Find the linearization L(x,y) of the function at each point. f(x,y) = x2 + y2 + 1 a. (4,0) b. (2,0) a. L(x,y) = Find the linearization L(x,y,z) of the function f(x,y,z) = 1x2 + y2 +z2 at the points (7,0,0), (3,4,0), and (4,4,7). The linearization of f(x,y,z) at (7,0,0) is L(x,y,z)= (Type an exact answer, using radicals as needed.)

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Find the equation of this line. y= [?]x+[?]

DochEvi [55]

Answer:

$y=3x-4$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x=0)

1) Determine the slope (m)

$m=\displaystyle\frac{y_2-y_1}{x_2-x_1}$ where two points that fall on the line are $(x_1,y_1)$ and $(x_2,y_2)$

On the graph, two points are highlighted for us: (0,-4) and (2,2). Plug these into the formula:

$m=\displaystyle\frac{2-(-4)}{2-0}\\\\m=\displaystyle\frac{2+4}{2}\\\\m=\displaystyle\frac{6}{2}\\\\m=3$

Therefore, the slope of the line is 3. Plug this into $y=mx+b$ :

$y=3x+b$

2) Determine the y-intercept (b)

$y=3x+b$

Recall that the y-intercept occurs when x=0. Given the point (0,-4), the y-intercept is therefore -4. Plug this into $y=3x+b$ :

$y=3x+(-4)\\y=3x-4$

I hope this helps!

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