1.9.17 Concavity and the second derivative (A-level only)

A curve $C$ has equation

2x^3 - 15x + \frac{k}{x}, \quad x > 0

where $k$ is a constant. The point $P$ with $x$ -coordinate $1$ lies on $C$ . Given that $P$ is a stationary point of $C$ :

show that $k = - 9$ .

[3]

Determine the nature of the stationary point at $P$ , justifying your answer.

[3]

The curve $C$ has a second stationary point.

Using algebra, find the $x$ -coordinate of this second stationary point.

[4]

1.9.17 Concavity and the second derivative (A-level only) Questions