Question

PART
2 points
39. A point x = xo is called a
stationary point of a function
f(x) if
O f(x) = 0
O f'(x) = x.
O f'(x) = 0
O f(x) = x.​

Answer 1

Answer:

don't know the answer.

Answer 2

TO DETERMINE

$\sf{A \: point \: x = x_0 \: is \: called \: a \: stationary \: point}$

$\sf{ of \: a \: function \: \: f(x) \: \: if \: \: at \: \: x = x_0\: }$

$\sf{1. \: \: \: f(x) = 0\: }$

$\sf{2. \: \: \: \: f \: '(x) =x}$

$\sf3. \: \: \: \: {f \: '(x) =0}$

$\sf{4. \: \: \: f \: (x) =x}$

CONCEPT TO BE IMPLEMENTED

STATIONARY POINT

DEFINITION

For a function f(x) a point c is said to be Stationary point if if the first order derivate of f(x) vanishes at x= c

In other words For a function f(x) a point c is said to be Stationary point if f'(c) = 0

Stationary point is a point of maximum or minimum or point of inflection

REASON FOR SUCH NAME

These points are called STATIONARY POINT as at these points the function is neither increasing nor decreasing.

GRAPHICAL REPRESENTATION

In graphical representation of f(x) such points corresponds to points where the tangent to the curve is a horizontal line

EVALUATION

Hence from above we can conclude that

$\sf{A \: point \: x = x_0 \: is \: called \: a \: stationary \: point}$

$\sf{ of \: a \: function \: \: f(x) \: \: if \: \: at \: \:x = x_0 }$

$\sf3. \: \: \: \: {f \: '(x) =0}$

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