Question

3.
If f (x, y) is differentiable function, then :
(A) only for exists
(B) both fx and fy exist
(C) only fy exists
(D) neither fx nor fy exist​

Answer 1

HELLO DEAR,

rolle's theorem and mean value theorem:-

rolle's theorem- Let f : [ a,b] --> R be continuous on [a,b] and differentiable on ( a,b) such that f(a)= f(b), where is a and b are some real numbers. Then, there exist at least one number c in ( a,b) such that

f'(c) = 0.

mean value theorem- Let f:[a,b] --> R be continuous function on [a,b] and differentiable on (a,b). Then, there exist at least one number c in (a,b) such that

f(b) - f(a)

f'(c) = ----------------

b - a

Therefore option (B) both fx and fy exist.

I HOPE IT'S HELP YOU DEAR,

THANKS.