Find out the stationary points of the function f(x)=x^2*e^(-2x)
Using the product rule (u'v+v'u, where u and v are the chosen substitutes) to find the first derivative will be dy/dx=x'=2xe^(-2x)+x^(2)e^(-2x)(-2)=2xe^(-2x)(x-x^2). This will give the details about the slope of the given function at any instance of time.If the stationary points are to be find the second derivative of the should be found as shown;d^(2)y/dx^2=2e^(-2x)(1-4x+2x^2). Stationary point will give the points where the gradient is zero.Therefore by saying d^(2)y/dx^2=0, the stationary points can be found and for this example those values are calculated as x=1+1/sqrt(2) and 1-1/sqrt(2).
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