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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

First, add the two fractions together. The common denominator is 2(x+1), or 2x+2. The first fraction becomes 6/(2x+2). The second fraction becomes (x+1)(3x-9)/(2x+2), or (3x²-6x -9)/(2x+2). Add...

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...

First, we want all the terms with X on one side, so let's +5 to both sides.3x² = 48Let's simplify, so we get x² on its own.48÷ 3=16x² = 16Now, we need x 'unsquared', so we...