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.
425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.