4.7 Use of differentiation to find maxima and minima points on a curve Quiz: AQA Further Maths, Unit 4

The 20 questions

1. At a stationary point on a curve, what is dy/dx?

   • Undefined
   • y
   • 0
   • 1

2. At a maximum point, what is the sign of d^2y/dx^2?

   • Zero
   • Negative
   • Undefined
   • Positive

3. At a minimum point, what is the sign of d^2y/dx^2?

   • Positive
   • 1
   • Negative
   • Zero

4. For y = x^2 - 4x + 1, at what x does the minimum occur?

   • x = 2
   • x = -2
   • x = 1
   • x = 4

5. What is the minimum value of y = x^2 - 4x + 1?

   • -1
   • 1
   • -3
   • 3

6. For y = -x^2 + 6x, at what x is there a maximum?

   • x = 6
   • x = 3
   • x = 0
   • x = -3

7. What is the maximum value of y = -x^2 + 6x?

   • -9
   • 9
   • 18
   • 3

8. y = x^3 - 3x has a stationary point at x = -1. What type of point is it?

   • Minimum
   • Not stationary
   • Point of inflection
   • Maximum

9. What is the y-value at the minimum of y = x^3 - 3x?

   • 0
   • 2
   • -1
   • -2

10. For y = 2x^2 + 8x + 5, what is the x-coordinate of the stationary point?

    • -8
    • 2
    • 4
    • -2

11. A rectangle has perimeter 20 and sides x and 10 - x. Which x gives the maximum area?

    • x = 4
    • x = 10
    • x = 5
    • x = 2

12. For y = x^3 - 6x^2 + 9x, what are the x-values of the stationary points?

    • x = -1 and x = -3
    • x = 1 and x = 3
    • x = 0 and x = 3
    • x = 2 and x = 4

13. For the curve y = x^3 - 6x^2 + 9x, which stationary point is a local maximum?

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

14. A stationary point where d^2y/dx^2 = 0 and the gradient does not change sign is called:

    • A minimum
    • A maximum
    • A point of inflection
    • An asymptote

15. What are the coordinates of the minimum point of y = x^2 + 16/x for x > 0?

    • (2, 12)
    • (2, 8)
    • (4, 8)
    • (8, 2)

16. Profit is P = -2x^2 + 12x - 5. At what x is profit maximised?

    • 12
    • 3
    • -3
    • 6

17. What is the maximum profit for P = -2x^2 + 12x - 5?

    • 18
    • 13
    • 5
    • -5

18. If dy/dx = 0 and d²y/dx² > 0 at a point, what type of point is it?

    • Asymptote
    • Minimum point
    • Maximum point
    • Point of inflection

19. What is the local minimum value of y = x^3 - 12x + 5?

    • -5
    • 11
    • -11
    • -19

20. What type of stationary point does y = x^4 - 8x^2 have at x = 0?

    • Local maximum
    • Point of inflection
    • Local minimum
    • No stationary point

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