If `f` is an odd continuous function in `[-1,1]` and differentiable in `(-1,1)` then

If f be a continuous function on [0,1] differentiable in (0,1) such that f(1)=0, then there exists some c in(0,1) such that

If f be a continuous function on [0,1], differentiable in (0,1) such that f(1)=0, then there exists some c in(0,1) such that

If f be a continuous function on [0,1], differentiable in (0,1) such that f(1) = 0 , then there exists some c in (0,1) such that

If f(x)=sqrt(1-sqrt(1-x^(2))), then f(x) is (a) continuous on [-1,1] and differentiable on (-1, 1) (b) continuous on [-1,1] and differentiable on (-1,0)uu varphi(0,1)(c) continuous and differentiable on [-1,1](d) none of these

If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] and differentiable on (-1, 1) (b) continuous on [-1, 1] and differentiable on ( − 1 , 0 ) ∪ ( 0 , 1 ) (c) continuous and differentiable on [-1, 1] (d) none of these

If f(x)=sqrt(1-(sqrt(1)-x^(2))), then f(x) is (a)continuous on [-1,1] and differentiable on (-1,1)(b) continuous on [-1,1] and differentiable on (-1,0)uu(0,1)(C) continuous and differentiable on [-1,1](d) none of these

If f(x) = sqrt(1-(sqrt1-x^2)) , then f(x) is (a)continuous on [-1, 1] and differentiable on (-1, 1) (b) continuous on [-1,1] and differentiable on (-1, 0) uu (0, 1) (C) continuous and differentiable on [-1, 1](d) none of these

Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then :

If f is continuous on [a,b] and differentiable in (a,b) then there exists c in(a,b) such that (f(b)-f(a))/((1)/(b)-(1)/(a)) is