4.9 Sketch/ interpret a curve with known maximum and minimum points Quiz: AQA Further Maths, Unit 4

The 20 questions

1. A curve has a local maximum at (2, 5) and crosses the y-axis at (0, 1). What is the y-value of the local maximum?

   • 0
   • 1
   • 2
   • 5

2. How does the sign of dy/dx change as x increases through a local minimum?

   • Negative to positive
   • Zero to negative
   • Positive to negative
   • Positive to zero

3. Where is the minimum point of y = (x - 1)(x - 3)?

   • (-2, 3)
   • (2, -1)
   • (2, 1)
   • (1, 0)

4. Where is the maximum point of y = -(x - 2)^2 + 4?

   • (2, -4)
   • (4, 2)
   • (-2, 4)
   • (2, 4)

5. A curve has a maximum at (1, 2) and a minimum at (3, -1). Is the curve increasing or decreasing between x = 1 and x = 3?

   • Decreasing
   • Constant
   • Stationary
   • Increasing

6. For y = x^3 - 3x, what is the y-value at the local maximum at x = -1?

   • 0
   • -2
   • 1
   • 2

7. If a curve has its minimum value at (4, 0), what is the minimum value of y?

   • -4
   • 0
   • Undefined
   • 4

8. Which shape describes a curve with a single minimum that rises on both sides?

   • N-shaped
   • Inverted U-shaped
   • Straight line
   • U-shaped

9. How many turning points can a cubic curve have at most?

   • One
   • Three
   • None
   • Two

10. For a curve with f'(x) > 0 for x < 2 and f'(x) < 0 for x > 2, what type of turning point is at x = 2?

    • Point of inflection
    • Minimum
    • No turning point
    • Maximum

11. For y = x^3 - 12x, what is the y-value at the local maximum?

    • -16
    • -8
    • 8
    • 16

12. For y = x^3 - 3x^2, at which x is there a local maximum?

    • x = 0
    • x = 1
    • x = 3
    • x = 2

13. For y = x^4 - 2x^2, which stationary point is a local maximum?

    • x = 2
    • x = 0
    • x = -1
    • x = 1

14. What is the y-value at the local minimum at x = 1 of y = x^4 - 2x^2?

    • -2
    • 0
    • 1
    • -1

15. A downward-opening parabola has a turning point at (3, 12). What nature is this point?

    • Maximum point
    • Y-intercept
    • Inflection point
    • Minimum point

16. For y = 2x^3 - 9x^2 + 12x, which x gives the local minimum?

    • x = 0
    • x = 3
    • x = 1
    • x = 2

17. For y = 2x^3 - 9x^2 + 12x, what is the y-value at the local maximum?

    • 7
    • 2
    • 4
    • 5

18. What is the gradient of the curve y = x³ - 3x at x = 0?

    • -1
    • 0
    • 3
    • -3

19. For f(x) = x + 4/x^2 with x > 0, at which x is there a local minimum?

    • 4
    • 2
    • 1
    • 8

20. What is the minimum value of f(x) = x + 4/x^2 for x > 0?

    • 2
    • 6
    • 4
    • 3

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