The power consumption, $w$ (in watts), of a submersible exploration drone at depth $d$ (in meters) is modelled by the equation

3d^3 - 40d + \frac{k}{d}, \quad d > 0

where $k$ is a constant. The drone has a stationary point in its power consumption at depth $P$ where $d = 2$ .

Show that $k = - 16$ .

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

The power consumption model suggests there is a second stationary point at a different depth.

Using algebra, find the depth of this second stationary point.

The power consumption, $w$ (in watts), of a submersible exploration drone at depth $d$ (in meters) is modelled by the equation

3d^3 - 40d + \frac{k}{d}, \quad d > 0

where $k$ is a constant. The drone has a stationary point in its power consumption at depth $P$ where $d = 2$ .

Show that $k = - 16$ .

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

The power consumption model suggests there is a second stationary point at a different depth.

Using algebra, find the depth of this second stationary point.

1.6 Differentiation

1.6 Differentiation Questions