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 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:[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: [a, b] -> 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 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 prime (x) = x has atleast one root in (a, b).

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] :