Stationary Point

A Resource for Free-standing maths Qualifications

Stationary Points

maximum

There be 3 types of unmoving points: maximum points, minimum points and points of inflection.

point of inflection

minimum

level best Points Consider what happens to the incline at a maximum point. It is validating just before the maximum point, zero at the maximum point, then forbid just after the maximum point. The note value of reassign of i.e.
dy is decreasing so the rate of dx
incline positive

gradient zero gradient detrimental

dy with respect to x is negative dx

d2 y is negative. dx 2

Minimum Points Just before a minimum point the gradient is negative, at the minimum the gradient is zero and just after the minimum point it is positive.
dy The value of is increasing so the rate of dx dy change of with respect to x is positive dx d2 y i.e. is positive. dx 2
gradient negative gradient zero gradient positive

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A Resource for Free-standing Mathematics Qualifications

Stationary Points

Points of Inflection dy d2 y At roughly points = 0 and = 0. dx dx 2 Two such points are shown in the sketches. They are called points of inflection. d2 y is also zero at close to dx 2 maximum and minimum points.



To find the type of stationary point, consider the gradient at each side of it. billet that
gradient positive

gradient positive

gradient zero gradient negative gradient zero

gradient negative

Sketching Curves consider the stationary point(s): dy Find an expression for and put it equal to 0, then solve the resulting equating to find dx the x co-ordinate(s) of the stationary point(s). d2 y Find and interpose each value of x to find the kind of stationary point(s). dx 2 (+ suggests a minimum, a maximum, 0 could be either or a point of inflection) Use the sophisticates equation to find the y co-ordinate(s) of the stationary point(s). Find the point(s) where the curve meets the axes: Substitute x = 0 in the...If you want to sound a full essay, order it on our website: Orderessay



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