The sufficient conditions for the function `f,RtoR` to be maximum at x=a will be

Using examples,prove that the condition (dy)/(dx)=0 is neither a necessary nor a sufficient condition for a function y=f(x) to have a maximum or a minimumat a point.

Write sufficient conditions for a point x=c to be a point of local maximum.

Write sufficient conditions for a point x=c to be a point of local maximum.

The function f:RtoR given by f(x)=|x|

The function f:RtoR defined by f(x)=e^(x) is

Let the function f: RtoR be defined by f(x)=2x+cosx . Then f

The function F:RtoR given by f(x)=-|x-1| is

Which one of the following functions f:RtoR is injective?

Statement 1 : For a continuous surjective function f: RtoR ,f(x) can never be a periodic function. Statement 2: For a surjective function f: RtoR ,f(x) to be periodic, it should necessarily be a discontinuous function.

Let alpha in R . Prove that a function f: RtoR is differentiable at alpha if and only if there is a function g:RtoR which is continuous at alpha and satisfies f (x) -f(alpha) = g (x) (x-alpha), AA x in R.