A function f is defined on an interval [a, b]. Which of the following statement(s) is are incorrect? (A) If f(a) and f(b) have opposite signs,then there must be a point `cin(a,b)` such that f(c)=0.

Consider a real valued continuous function f(x) defined on the interval [a, b). Which of the followin statements does not hold(s) good? (A) If f(x) ge 0 on [a, b] then int_a^bf(x) dx le int_a^bf^2(X)dx (B) If f (x) is increasing on [a, b], then f^2(x) is increasing on [a, b]. (C) If f (x) is increasing on [a, b], then f(x)ge0 on (a, b). (D) If f(x) attains a minimum at x = c where a lt c lt b, then f'(c)=0.

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) (iii)If a (a)Only I and II (b)Only I and III (c)Only II and III (d)Only III

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) (iii)If a (a)Only I and II (b)Only I and III (c)Only II and III (d)Only III

The function f(x) is defined on the interval [0,1]. What are the domains of definition of functions. (a) f(sin x), (b) f(2x+3)?

If f is an odd function and f(a)=b , which of the following must also be true ? I. f(a)=-b II. f(-a)=b III. f(-a)=-b

Let f be continuous and differentiable function such that f(x) and f(x) have opposite signs evergywhere . Then

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)

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 .