If the function `f(x) and g(x)` are continuous in [a, b] and differentiable in (a, b), then the f(a) f (b) equation `|(f(a),f(b)),(g(a),g(b))|=(b-a)|(f(a),f'(x)),(g(a),g'(x))|` has, in the interval `[a,b]` :

If the functions f(x) and g(x) are continuous on [a,b] and differentiable on (a,b) then in the interval (a,b) the equation |{:(f'(x),f(a)),(g'(x),g(a)):}|=(1)/(a-b)=|{:(f(a),f(b)),(g(a),g(b)):}|

If f(x) and g(x) are continuous functions in [a,b] and are differentiable in (a,b) then prove that there exists at least one c in(a,b) for which.det[[f(a),f(b)g(a),g(b)]]=(b-a)det[[f(a),g'(c)]], where a

if f(x) and g(x) are continuous functions, fog is identity function, g'(b) = 5 and g(b) = a then f'(a) is

Let f and g be function continuous in [a,b] and differentiable on [a,b] If f(a)=f(b)=0 then show that there is a point c in(a,b) such that g'(c)f(c)+f'(c)=0

If f and g are both continuous at x = a, then f-g is

If f(x) and g(x) are two continuous functions defined on [-a,a], then the value of int_(-a)^(a){f(x)+f(-x)}{g(x)-g(-x)}dx is

PARAGRAPH : If function f,g are continuous in a closed interval [a,b] and differentiable in the open interval (a,b) then there exists a number c in (a,b) such that [g(b)-g(a)]f'(c)=[f(b)-f(a)]g'(c) If f(x)=e^(x) and g(x)=e^(-x) , a<=x<=b c=

If the function f(x):A to B and g(x):B to C are defined such that (g(f(x)))^-1 exist then f(x) and g(x) are