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

Write necessary condition for a point x=c to be an extreme point of the function f(x)

Write necessary condition for a point x=c to be an extreme point of the function f(x) .

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.

Is every critical point, a point of local maximum or local minimum.

The function f(x)=(|x^(2)-2|)/(|x^(2)-4|) has,(a) no point of local maxima (b) no point of local minima (c) exactly one point of local minima (d) exactly one point of local maxima

The function f(x)=|x^2-2|/|x^2-4| has, (a) no point of local maxima (b) no point of local minima (c) exactly one point of local minima (d) exactly one point of local maxima

Let x=c be a point in the domain of definition of a differentiable function , then f(x) will have a local maximum at x=c when -

Find the point of local maxima and local minima of the function f(x) = sin x - cos x, 0 lt x lt 2pi . Also, find the local maximum and local minimum values.

Find the points of local maxima or local minima and the corresponding local maximum and minimum values of each of the following functions: f(x) = (x -3)^(4)