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

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

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)

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 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 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 be a differentiable function on the open interval(a, b). Which of the following statements must be true? (i) f is continuous on the closed interval [a,b], (ii) f is bounded on the open interval (a,b) (iii)If a (a)Only I and II (b)Only I and III (c)Only II and III (d)Only III

Let f be a differentiable function on the open interval(a, b). Which of the following statements must be true? (i) f is continuous on the closed interval [a,b], (ii) f is bounded on the open interval (a,b) (iii)If a (a)Only I and II (b)Only I and III (c)Only II and III (d)Only III

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 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 be continuous on [a , b],a >0,a n d differentiable on (a , b)dot Prove that there exists c in (a , b) such that (bf(a)-af(b))/(b-a)=f(c)-cf^(prime)(c)