Mathematics B (MEI) H630: CALCULUS Topical Past Paper Questions

Determine the range of values of x for which $ y = 4x^{3} + 7x^{2} - 6x + 8 $ is a decreasing function. [5]

In this question you must show detailed reasoning. The equation of a curve is $ y = 16\sqrt{x} + \frac{8}{x} $. Determine the equation of the tangent to the curve at the point where x = 4. [7]

In this question you must show detailed reasoning. The equation of a curve is $ y = 3x + \frac{7}{x} - \frac{3}{x^{2}} $. Determine the coordinates of the points on the curve where the curve is parallel to the line y = 2x. [9]