calc_tutorial_14_4_007

 
Problem Statement

{3,4,5,6,7,8,9}
pow(3,2)+1
2*3
-((pow(3,2)+6)/2)
((pow(3,2)+6)/2)
((pow(3,2)-8)/2)

Find an equation of the tangent plane to

at the point .

 
Step 1

Question Sequence

Question 1

Recall how to find the equation of the tangent plane to a surface at a given point. Assume that f(x, y) is defined in a disk D containing (a, b) and that fx(a, b) and fy(a, b) exist. Then the tangent plane to the graph at (a, b, f(a, b)) is the plane defined by the following equation.

A.
B.

Note that it is necessary that fx(a, b) and fy(a, b) exist to use this equation. We can check that they exist by ensuring that f(x, y) is differentiable on an open disk D containing (a, b). To do so, we use the fact that f(x, y) is differentiable on an open disk D provided that fx(x, y) and fy(x, y) exist and are continuous on an open disk D.

Given , find and .

A.
B.

A.
B.

and are both defined for and .

Therefore be differentiable on an open disk containing the point (3, 1).

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Find F(3, 1), Fr(3, 1) and Fs(3, 1).

F(3, 1) =

Fr(3, 1) =

Fs(3, 1) =

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 3

Use information from the previous steps to write the equation of the tangent plane to

at the point .

= r - s -

Correct.
Incorrect.