Find the coordinates of the stationary points of the curve 3x=y+6x+3

First, straight away from reading the question you know this question will involve differentiating the function with respect to x so immediately you want to re-write the equation in terms of y which in this case y=3x^(2)-6x-3.From the question the question the key word stationary points should be jumping out to you and from this you should know that you'll need to differentiate the re-arranged function.Doing this you get dy/dx=6x-6 and in an exam situation the bulk of the marks will be yours.To tie up this particular question you now need to find the value of x which makes 6x-6=0 since at the stationary points the rate of change (dy/dx) or the gradient is 0.From this we can see that 6x=6 and hence x=1, plugging this into the equation of the curve we find that y=-6 and therefore the stationary point is (1,-6).