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secondary 4 | A Maths
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how to do B2ii?
Date Posted: 3 years ago
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you can use first or second derivative test to find the nature of the stationary point.
first derivative test is taking the x coordinate of the point and testing its neighbours, whether the derivative of them are positive or negative. it will be easier to draw out a simple table, for example:
x- x x+
dy/dx 1.5 0 -2
slope of curve / ___ \
so in this example the stationary point is a maximum. if dy/dx for x- is negative and x+ is positive, the stationary point is a minimum. if dy/dx for x- and x+ are both positive or negative, the stationary point is a point of inflexion.
second derivative test is to find d^y/dx^2 by differentiating the equation 2 times. if d^y/dx^2 > 0, the stationary point is a minimum. if d^y/dx^2 < 0, the stationary point is a maximum.
hope this helps
first derivative test is taking the x coordinate of the point and testing its neighbours, whether the derivative of them are positive or negative. it will be easier to draw out a simple table, for example:
x- x x+
dy/dx 1.5 0 -2
slope of curve / ___ \
so in this example the stationary point is a maximum. if dy/dx for x- is negative and x+ is positive, the stationary point is a minimum. if dy/dx for x- and x+ are both positive or negative, the stationary point is a point of inflexion.
second derivative test is to find d^y/dx^2 by differentiating the equation 2 times. if d^y/dx^2 > 0, the stationary point is a minimum. if d^y/dx^2 < 0, the stationary point is a maximum.
hope this helps
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