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Quiz

Year 4: Derivatives

10 questions with solutions for year 4: computing derivatives, tangents and normals, speed and acceleration, extrema, points of inflection, optimisation – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. The derivative of f(x) = 4x³ − (1/2)x² + 3x − 2 is:

2. The derivative of f(x) = ln((3x − 2)/(x + 1)) is:

3. Tangent to y = 4x − x² at x = 2:

4. Normal to f(x) = x³ − 2x + 1 at x = −1:

5. s(t) = t³ − 2t² + 4t. What is the speed at t = 2?

6. s(t) = 3t³ + t² − 5. What is the acceleration at t = 1?

7. The local minimum of f(x) = 2x³ − 6x² is:

8. The point of inflection of f(x) = x³ − 3x² is:

9. Split 60 into two parts with the largest product. What is the product?

10. Of all rectangles with perimeter 44 cm, what is the largest area (cm²)?