Prove. If f , f x , and f y are continuous on a circular region containing A x 0 , y 0 and B x 1 , y 1 , then there is a point x ∗ , y ∗ on the line segment joining A and B such that . f x 1 , y 1 − f x 0 , y 0 = f x x ∗ , y ∗ x 1 − x 0 + f y x ∗ , y ∗ y 1 − y 0 This result is the two-dimensional version of the Mean-Value Theorem.
Prove. If f , f x , and f y are continuous on a circular region containing A x 0 , y 0 and B x 1 , y 1 , then there is a point x ∗ , y ∗ on the line segment joining A and B such that . f x 1 , y 1 − f x 0 , y 0 = f x x ∗ , y ∗ x 1 − x 0 + f y x ∗ , y ∗ y 1 − y 0 This result is the two-dimensional version of the Mean-Value Theorem.
Prove. If
f
,
f
x
,
and
f
y
are continuous on a circular region containing
A
x
0
,
y
0
and
B
x
1
,
y
1
,
then there is a point
x
∗
,
y
∗
on the line segment joining A and B such that .
f
x
1
,
y
1
−
f
x
0
,
y
0
=
f
x
x
∗
,
y
∗
x
1
−
x
0
+
f
y
x
∗
,
y
∗
y
1
−
y
0
This result is the two-dimensional version of the Mean-Value Theorem.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY