How do you find stationary points of an equation, eg. y=x^2+3x+2
Stationary points of an equation are found where the gradient of the tangent at this point equals zero. A diagram can illustrate this. To find them differentiate the given equation (which gives the gradient) and set this to zero. eg. dy/dx = 2x+32x+3=0x=-3/2Plug this back into the equation of the line to find the y valuey=(-3/2)^2 + 3(-3/2) +2y= -1/4Stationary point is (-3/2, -1/4)To find the nature of this stationary point, find the second derivative, plug in your x value. If the value of the second derivative if positive, the point is a minimum, negative means a maximum.
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