Practice Calculus (3) - Calculus - ICSE 12 Mathematics

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9 questions

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6 sample questions

Question 1.
What is the derivative of f(x) = 3x^2?
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Apply the Power Rule.
Question 2.
If f(x) = x + 5, what is f'(x)?
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Constant terms have a derivative of zero.
3Question 3.
What is the derivative of f(x) = x^3?
- 3x^2
- x^2
- 3x
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Use the Power Rule.
4Question 4.
True or False: The derivative of a constant is always one.
- True
- False
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Remember that constants do not change.
Question 5.
A car's position is given by s(t) = t^3 - 6t^2 + 9t. Find the time(s) when the velocity of the car is zero.
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Set the derivative equal to zero.
Question 6.
You have a rectangular garden where the length is twice the width. If the width increases at a rate of 1m/s, find the rate at which the area is increasing when width = 5m.
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Use implicit differentiation for areas.

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