A function ggg is defined by g(x)=x3x−6g(x) = \frac{x}{\sqrt{3x - 6}}g(x)=3x−6x.
State the maximum possible domain of ggg.
Use the quotient rule to show that g′(x)=3x−122(3x−6)32g'(x) = \frac{3x - 12}{2(3x - 6)^{\frac{3}{2}}}g′(x)=2(3x−6)233x−12.
Show that the graph of y=g(x)y = g(x)y=g(x) has exactly one point of inflection.
Write down the values of xxx for which the graph of y=g(x)y = g(x)y=g(x) is concave.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.