If a function `f` is continuous for all x and if f has a relative maximum at `(-1,4)` and a relative minimum at `(3,-2)`, then which of the following statements must be true?

Which of the following statement is/are always true concerning the function f(x)=x+1/x (I)The graph of the function is symmetric about the y-axis. (II)The graph of the function has a relatively maximum at (1, 2) and a relative minimum at (-1,\ -2)dot (III)The graph of the function is concave up for x >0 and concave down for x<0. (a)only I (b) only II (c)only III (d) only I and II

The function f is a parabolic function that intersects the x-axis. Which of the following statements must be true ?

Let F(x) be such that F((1-x)/(1+x))=x for all x!=-1 which of the following statements is true

If a differentiable function f(x) has a relative minimum at x = 0, then the function y=f(x) +ax+b has a relative minimum at x = 0 for :

A cubic polynomial y=f(x) has a relative minimum at x=1& maximum at x=-2. If f(0)=1 then

If f(x) be a function defined in neighborhood of a and f'(a)=0 . If f(x) has relative maximum at x=a , then what can be said about f''(a) .

If a differentiable function f(x) has a relative minimum at x=0, then the function g = f(x) + ax + b has a relative minimum at x =0 for

A differentiable function f(x) has a relative minimum at x=0 Then the funiction y=f(x)+ax+b has a relative minimum at x=0 for

Let f(x) be twice differentiable function for all real x and f(1) = 1, f(2) = 4 , f(3) = 9. Then which one of the following statements is definitelly true ?

Let f be a function which is continuous and differentiable for all real x. If f(2) = -4 and f'(x) ge 6 for all x in [2,4] , then