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y = (3x^3+2x+7)/x^(1/2) = 3x^(5/2)+2x^(1/2)+7x^(-1/2)dy/dx = 15/2x^(3/2)+x^(-1/2)-3.5x^(-3/2)

i) 5x^4 + 3/2x^1/2 + 1ii) 1/6x^6 + 2/5x^5/2 + 1/2x^2 + 7x + c

The second differential of the equation of the curve will be positive if it is convex. This is because, by definition, convex means that the gradient of a curve is increasing. To find the gradient of a cu...

"Solve the simultaneous equations" is another way of saying find the unknown variables. In this case, they are x and y. When looking at the second equation, y^2+5x^2+2x=0, we can see that we hav...

For this question we already have the derivative of f(x), and so if we integrate it we should get to a general equation with a constant on the end, however we want to get to an exact solution which we sho...