Differential Calculus is one of 9 topics in the Grade 12 Technical Mathematics CAPS syllabus, covered across 3 lessons on Study Vault. Below are real practice questions from this topic with full worked answers.
Sample practice questions
Easy
1. What does the derivative f'(x) represent, geometrically?
The gradient of the tangent line to the graph of f at x
The y-intercept of the graph of f
The x-intercept of the graph of f
The area under the graph of f
Answer: The gradient of the tangent line to the graph of f at x — The derivative f'(x) represents the gradient of the tangent line to the graph of f at the point x.
Easy
2. Using first principles, what is f'(x) if f(x) = k, a constant?
0
k
1
x
Answer: 0 — For a constant function, [f(x+h)-f(x)]/h = (k-k)/h = 0 for all h, so f'(x) = 0.
Medium
3. State the first-principles definition of f'(x) as a limit.
Answer: f'(x) = lim h->0 [f(x+h) - f(x)] / h — By definition, f'(x) = lim(h->0) [f(x+h) - f(x)] / h.
