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This question involves inspecting the answers that have been provided to us. We have been given a constant gradient, and a point at which the line given by the equation cuts the y axis. This, therefore, m...

In order to solve the equation, we need to find a way to break the '7x' term in the middle that allows factorisation. We also need to consider the fact that the last term '-3x' has a minus sign. This broa...

^{Firstly rearrange the equation so that only dy/dx is on the left hand sidedy/dx = (x/(1+x^2)) tan(y)Now separate the variables such that the x terms are on one side with the dx,...}

The stationary point is a minimum point. I will run through the working out for the question using the whiteboard in the session as it is difficult to demonstrate without relevant formatting.

This requires use of the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)^2]dy/dx = ([(3x-1)*2x] - 3x^2)/[(3x-1)^2],= (3x^2-2x)/[(3x-1)^2],=[x(3x-2)]/[(3x-1)^2]