Home
Class 12
MATHS
Let f:[a, b] rarrR be such that f is dif...

Let `f:[a, b] rarrR` be such that f is differentiable in (a, b), f is continuous at x = a & x = b and moreover `f(a)=0=f(b)`. Then

A

there exists at least one point `c in (a,b)` for which f(c ) = f(c )

B

f'(x) = f(x) does not hold at any point of (a,b)

C

at every point of (a,b), f'(x) `gt f(x)`

D

at every point of `(a, b), f'(x) lt f(x)`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

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(x) and g(x) be differentiable function in (a,b), continuous at a and b, and g(x)!=0 in [a,b]. Then prove that (g(a)f(b)-f(a)g(b))/(g(c)f'(c)-f(c)g'(c))=((b-a)g(a)g(b))/((g(c))^(2))

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

Let f be a function from [a,b] to R , (where a, b in R ) f is continuous and differentiable in [a, b] also f(a) = 5, and f'(x) le 0 for all x in [a,b] then for all such functions f, f(b) + f(lambda) lies in the interval where lambda in (a,b)

Let f : R rarr R satisfying l f (x) l <= x^2 for x in R, then (A) f' is continuous but non-differentiable at x = 0 (B) f' is discontinuous at x = 0 (C) f' is differentiable at x = 0 (D) None of these

Statement-1 : If f is differentiable on an open interval (a,b) such that |f'(x)le M "for all" x in (a,b) , then |f(x)-f(y)|leM|x-y|"for all" in (a,b) Satement-2: If f(x) is a continuous function defined on [a,b] such that it is differentiable on (a,b) then exists c in (a,b) such that f'(c)=(f(b)-f(a))/(b-a)

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

Let f(x)=ax+1,x For what values of a and b is f(x) continuous at x=1