Download Worksheet 13.2

Maths Quest Maths B Year 11 for Queensland
WorkSHEET 13.2
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Chapter 13 Differentiation and application WorkSHEET 13.2
Differentiation and applications
If f x   x 2  2 x  8 , find:
(a) the average rate of change between x = 3
and x = 6
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Name: _____________________
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(b) a function which describes the rate of
change
(c) the instantaneous rate of change at x = 3.
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If the position of a vehicle is given by the
equation xt   2t 2  20t , find:
(a) the average rate of change (velocity)
between t = 1 and t = 3
(b)
a function which describes the velocity
(c)
the instantaneous velocity at t = 3.
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3
For the vehicle in the previous question, find:
(a) the average rate of change (velocity)
between t = 6 and t = 8
(b)
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the instantaneous velocity at t = 8.
Why are your answers to question 3 positive,
yet the answers to question 2 were negative?
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Maths Quest Maths B Year 11 for Queensland
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Chapter 13 Differentiation and application WorkSHEET 13.2
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For the vehicle in the previous question, find
when and where the velocity is zero.
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A large snowball is melting according to the
equation V t   144  t 2 , find:
(a) the average rate of change between t = 4
and t = 9
(b)
a function which describes the rate of
change
(c)
the instantaneous rate of change at t = 9.
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A projectile is fired with a trajectory equation
of: H x   20  8 x  x 2 , x  [0, 10] where H is
the vertical height and x is the horizontal
displacement (both distances measured in
metres).
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What is the maximum height and at what
horizontal displacement does it occur?
Sketch the path of the projectile.
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Maths Quest Maths B Year 11 for Queensland
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Chapter 13 Differentiation and application WorkSHEET 13.2
The profit ($p) to be earned by a small
company per day is related to the number of
employees (x), according to the equation
px   2000  216 x  2 x3 , x  [1, 10]
What is the maximum number of employees for
maximum profit? What is the maximum profit?
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Sketch the profit function.
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A farmer plans to use a river as one boundary
of a rectangular paddock. If the farmer has
480 m of fencing to be used to fence the other 3
sides, what dimensions should the paddock be
to ensure maximum area?
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What numbers, when squared and added to
their own squared reciprocals, lead to a
minimum value?
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Maths Quest Maths B Year 11 for Queensland
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Chapter 13 Differentiation and application WorkSHEET 13.2
The sum of two numbers is 10. What are the
two numbers if the sum of their squares is a
minimum?
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