1.6.4 Differentiation

The profit $P$ , in thousands of pounds, generated by a chemical plant is modeled by the equation

54v^{\frac{1}{2}} - 2v^{\frac{3}{2}} + 10, \quad v > 0

where $v\,$ is the volume of a specific catalyst used in litres.

Find $dPdv\dfrac{dP}{dv}$ , giving each term in its simplest form.

[2]

Hence find the coordinates of the stationary point of the profit model.

[3]

Find $d2Pdv2\dfrac{d^2 P}{dv^2}$ and hence determine the nature of this stationary point.

[3]

1.6.4 Differentiation Questions

The profit $P$ , in thousands of pounds, generated by a chemical plant is modeled by the equation

54v^{\frac{1}{2}} - 2v^{\frac{3}{2}} + 10, \quad v > 0

where $v\,$ is the volume of a specific catalyst used in litres.

Find $dPdv\dfrac{dP}{dv}$ , giving each term in its simplest form.

[2]

Hence find the coordinates of the stationary point of the profit model.

[3]

Find $d2Pdv2\dfrac{d^2 P}{dv^2}$ and hence determine the nature of this stationary point.

[3]