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1.7.17 Product and quotient rules (A-level only)

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Question 5

A function ggg is defined by g(x)=x3x−6g(x) = \frac{x}{\sqrt{3x - 6}}g(x)=3x−6​x​.

a.

State the maximum possible domain of ggg.

[2]
b.

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)23​3x−12​.

[4]
c.

Show that the graph of y=g(x)y = g(x)y=g(x) has exactly one point of inflection.

[5]
d.

Write down the values of xxx for which the graph of y=g(x)y = g(x)y=g(x) is concave.

[2]

1.7.17 Product and quotient rules (A-level only) Questions

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