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1.10.3 Applications of differentiation

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Question 31

The power consumption PPP (in kW) of an industrial extractor fan is modelled by the equation

P=13w3−6w+kw,w>0 P = \frac{1}{3}w^3 - 6w + \frac{k}{w}, \quad w > 0 P=31​w3−6w+wk​,w>0

where www is the angular velocity in rad/s and kkk is a constant. The fan is observed to have a stationary point in its power profile when w=2w = 2w=2.

a.

Show that k=−8k = -8k=−8.

[3]
b.

Determine the nature of the stationary point when w=2w = 2w=2, justifying your answer.

[3]
c.

The power profile has a second stationary point.

Using algebra, find the exact value of the angular velocity www at this second stationary point.

[3]

1.10.3 Applications of differentiation Questions

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