1.6 Differentiation

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Question 20

Sketch the graph of any cubic function that has both three distinct real roots and a negative coefficient of $x^3$ .

[1]

bi.

The function $g (x)$ is defined by

g(x) = x^3 - 4ax^2 + k

where $a$ and $k$ are constants and $a > 0$ .

Show that there is a stationary point where the curve crosses the $y$ -axis.

[2]

bii.

Given that the equation $g (x) = 0$ has three distinct real roots, find the range of possible values for $k$ in terms of $a$ by considering the positions of the local maximum and local minimum points.

[4]

Sketch the graph of any cubic function that has both three distinct real roots and a negative coefficient of $x^3$ .

[1]

The function $g (x)$ is defined by

g(x) = x^3 - 4ax^2 + k

where $a$ and $k$ are constants and $a > 0$ .

Show that there is a stationary point where the curve crosses the $y$ -axis.

[4]

1.6 Differentiation

Question 20

Markscheme

1.6 Differentiation

Question 20

Markscheme

1.6 Differentiation

Question 20

1.6 Differentiation Questions

1.6 Differentiation

Question 20

1.6 Differentiation Questions