Mathematics Pure Math 1 9709: DIFFERENTIATION Topical Past Paper Questions

A function f is defined by $ f(x) = 3 - \frac{4}{2x + 3} $ for $ x > -\frac{3}{2} $. (a) (i) Find $ f'(x) $. (ii) Hence, show that f is an increasing function. (b) (i) Find an expression for $ f^{-1}(x) $. (ii) State the domain and range of $ f^{-1} $

The diagram shows the curve with equation $ y = 4x^2 - x^3 $ and the tangent to the curve at the point $ P $. The point $ P $ has $ x $-coordinate 3. (a) Find the equation of the tangent to the curve at the point $P$. Give your answer in the form $y = mx + c$. [5] (b) The shaded…

The equation of a curve is $ y = kx^{\frac{1}{2}} - 4x^{2} + 2 $, where k is a constant. (a) Find $ \frac{dy}{dx} $ and $ \frac{d^{2}y}{dx^{2}} $ in terms of k. [2] (b) It is given that k = 2. Find the coordinates of the stationary point and determine its nature. [4] (c) Points $…