Practice What Is A Derivative? (1.1) - Derivatives - IB 10 Mathematics

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6 sample questions

Question 1.
What is the derivative of a constant function f(x) = 3?
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Remember that constants do not change.
Question 2.
Using the power rule, find the derivative of f(x) = x^4.
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Apply the power rule: multiply by the exponent and reduce the exponent by 1.
3Question 3.
What does the derivative of a function represent?
- The height of the function
- The rate of change of the function
- The area under the function
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Consider how speed relates to distance over time.
4Question 4.
True or False: The derivative of a constant function is always 1.
- True
- False
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Think of a line with no slope.
Question 5.
Prove that the derivative of f(x) = 1/x is f'(x) = -1/x^2 using the limit definition.
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Be careful with the algebra when combining fractions.
Question 6.
Find the second derivative of f(x) = 3x^4 - 5x^2 + x.
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Derivatives can be taken multiple times, just apply the rules successively.

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