Question

Let f(x,y)=3xy−5x^{2}−2y^{2}

Then an equation for the tangent plane to the graph of ff at the point (3,3)(3,3) is

Answer #1

LET F(x,y) = ycos(x-y) . Determine the equation of the tangent
plane to F at point (2,2,2). Then, determine the linear
approximation of F near (2,2). How can you justify that this is
correct?

Consider the function f(x,y)=y+sin(x/y)
a) Find the equation of the tangent plane to the graph offat the
point(1,3)
b) Find the linearization of the function f at the point(1;3)and
use it to approximate f(0:9;3:1).
c) Explain why f is differentiable at the point(1;3)
d)Find the differential of f
e) If (x,y) changes from (1,3) to (0.9,3.1), compare the values
of ‘change in f’ and df

Let f(x, y) = x tan(xy^2) + ln(2y). Find the equation of the
tangent plane at (π, 1⁄2).

1. Find the equation of the tangent plane to the function f ( x,
y ) = x^2 + y^2 at the point (1,1).
2. Find a different solution to Laplace's equation.

Find an equation of the plane tangent to the surface
x3 - 2y2 + z4 = 5 at the point
P(1, -1, 1)

Find the relative extreme values of the function.
f(x, y) = 3xy − 2x2 − 2y2 + 14x − 7y −
2

Let f(x)=22−x2f(x)=22-x2
The slope of the tangent line to the graph of f(x) at the point
(−4,6) is .
The equation of the tangent line to the graph of f(x) at (-4,6) is
y=mx+b for
m=
and
b=
Hint: the slope is given by the derivative at x=−4

f(x,y)=x^2+4xy-y^2 find an equation for the tangent
plane at the surface point (2,1,11)

Find an equation of the tangent plane to the surface x y 2 + 3 x
− z 2 = 4 at the point ( 2 , 1 , − 2 ) An equation of the tangent
plane is

let f(x) = sqrt x^4+4x+4.find the equation of the tangent line
to the graph of f −1(a) when a = 3

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