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^{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,...}

If 168 is four sevenths of a number then divide this by 4 to give 1 seventh of the number.
168/4 = 42
So 42 is one seventh of the number.
Now multiply this by 7 to find the number.
42*...

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]

y = x³ - 3x² - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x² - 6x -24 = 0 -> x² - 2x - 8 = 0 -> (x+2)(x-4) = 0Th...