Mathematics 7357: Differentiation Topical Past Paper Questions

A curve has equation $ y = x^{4} + 2x $ Find an expression for $ \frac{dy}{dx} $ [2 marks]

A water slide is the shape of a curve PQ as shown in Figure 1 below. Figure 1 The curve can be modelled by the parametric equations $$ x=t-\frac{1}{t}+4.8 $$ $$ y=t+\frac{2}{t} $$ where $ 0.2 \leq t \leq 3 $ The horizontal distance from O is x metres. The vertical distance above…

The function f is defined by $$ \mathrm{f}(x)=\frac{x^{2}+10}{2x+5} $$ where f has its maximum possible domain. The curve $y = f(x)$ intersects the line $y = x$ at the points $P$ and $Q$ as shown below. (a) State the value of x which is not in the domain of f. [1 mark] [1 mark] )…