Continuity in open interval and closed interval

Continuity in open & closed interval || Built in limit || Continuity at boundary points || Different illustration OF continuity

Define a continuous function on the closed interval [a,b]

Maxima and minima in close interval

Let f(x), be a function which is continuous in closed interval [0,1] and differentiable in open interval 10,1[ Show that EE a point c in]0,1[ such that f'(c)=f(1)-f(0)

Define the continuity of f(x)" at " x= a . When is the function said to be continuous in the closed interval alexleb ?

PARAGRAPH : If function f,g are continuous in a closed interval [a,b] and differentiable in the open interval (a,b) then there exists a number c in (a,b) such that [g(b)-g(a)]f'(c)=[f(b)-f(a)]g'(c) If f(x)=e^(x) and g(x)=e^(-x) , a<=x<=b c=

Continuity in interval , Continuity at point function , Limit based continuity questions, Important points

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)