If f is a continuous function on `[a, b]` and `u(x)` and `v(x)` are differentiable functions o

If f(x) is continuous function , then

is f(x)=|x| a continuous function?

If y = f(u) is a differentiable functions of u and u = g(x) is a differentiable functions of x such that the composite functions y = f[g(x) ] is a differentiable functions of x then (dy)/(dx) = (dy)/(du) . (du)/(dx) Hence find (dy)/(dx) if y = sin ^(2)x

If y =f(u) is differentiable function of u, and u=g(x) is a differentiable function of x, then prove that y= f [g(x)] is a differentiable function of x and (dy)/(dx)=(dy)/(du)xx(du)/(dx) .

If f(t) is a continuous function defined on [a,b] such that f(t) is an odd function, then the function phi(x)=int_(a)^(x) f(t)dt

Which of the following is not true? (A) A polynomial function is always continuous (B) A continuous function is always differentiable (C) A differentiable function is always continuous (D) None of these

If f(x) is twice differentiable and continuous function in x in [a,b] also f'(x) gt 0 and f ''(x) lt 0 and c in (a,b) then (f(c) - f(a))/(f(b) - f(a)) is greater than

If f(x) be continuous function and g(x) be discontinuous, 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)