Tet f be continuous on [a, b] and differentiable on `(a,b).` If `f(a)=a and f(b)=b,` then

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

Let f:[a,b]rarr R be a function,continuous on [a,b] and twice differentiable on (a,b). If,f(a)=f(b) and f'(a)=f'(b), then consider the equation f''(x)-lambda(f'(x))^(2)=0. For any real lambda the equation hasatleast M roots where 3M+1 is

Let f be continuous on [a;b] and differentiable on (a;b) If f(x) is strictly increasing on (a;b) then f'(x)>0 for all x in(a;b) and if f(x) is strictly decreasing on (a;b) then f'(x)<0 for all x in(a;b)

Let f be continuous on [a,b] and differentiable on (a,b). then,which of the following statements is FALSE?

Let f be arry continuously differentiable function on [a,b] and twice differentiable on (a.b) such that f(a)=f(a)=0 and f(b)=0. Then

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)):}|

Let f be continuous on [a,b],a>0, and differentiable on (a,b). Prove that there exists c in(a,b) such that (bf(a,b))/(b-a)=f(c)-cf'(c)

Let f is continuous on [a,b] and differentiable on (a,b)s.t.t^(2)(a)-t^(2)(b)=a^(2)-b^(2) .Show that....f(x)f^(2)(x)=x has atleast one root in (a,b).