UNDERSTAND · PRACTISE · REVIEW
A derivative describes instantaneous rate of change. Practise the power rule with small expressions, then evaluate at a stated input. Do not confuse a derivative function with its value at one point.
A worked example
Try this learning routine
- Read the explanation and say the idea in your own words.
- Cover the worked answer and attempt a similar question.
- Check each step, including units or word meaning.
- Record one mistake and retry a new example later.
Independent practice
Choose one answer for each question and write a reason. These are foundation activities, not a complete board examination.
For f(x)=3x², find f′(3).
For f(x)=4x², find f′(4).
For f(x)=5x², find f′(5).
For f(x)=6x², find f′(6).
For f(x)=7x², find f′(2).
For f(x)=8x², find f′(3).
Answers and explanations
- 18 — f′(x)=2(3)x; substitute x=3 to obtain 18.
- 32 — f′(x)=2(4)x; substitute x=4 to obtain 32.
- 50 — f′(x)=2(5)x; substitute x=5 to obtain 50.
- 72 — f′(x)=2(6)x; substitute x=6 to obtain 72.
- 28 — f′(x)=2(7)x; substitute x=2 to obtain 28.
- 48 — f′(x)=2(8)x; substitute x=3 to obtain 48.
Your next step
Use the same idea in a fresh example. Bring the method and your questions to a discussion with TRICEF, rather than relying on a score alone.
Original TRICEF Academy practice material. Not an official board paper. Open the answer section before printing if you want the answer key included.