Find dy/dx for y = x² + 4x

[2 marks]

Solve dy/dx = 0 for y = x² - 10x

[3 marks]

Find the x-coordinate of the turning point of y = 3x² + 6x

[3 marks]

State whether y = x² has a maximum or minimum turning point.

[1 marks]

Find the gradient of y = 5

[1 marks]

Find the coordinates of the turning point for y = x² - 4x + 9

[4 marks]

Find the turning points of the cubic y = x³ - 3x

[5 marks]

Determine the nature of the turning point at x = 2 for y = -x² + 4x

[3 marks]

Find the x-values where the gradient of y = ⅓x³ - x² - 3x is zero.

[4 marks]

A curve has gradient function dy/dx = 3x² - 12. Find the stationary points.

[5 marks]

Show that y = x³ + x has NO stationary points.

[3 marks]

Box Problem: A box has volume V = 4x³ - 10x² cm³ where x > 0. Find the value of x that gives maximum volume.

[6 marks]

Perimeter constraint: A rectangle has perimeter 40 cm. If width is x cm, show that area A = 20x - x². Find x for maximum area.

[6 marks]

Kinematics Link: A particle's velocity is v = 3t² - 12t m/s. Find when velocity is minimum and state the minimum velocity.

[5 marks]

Second Derivative: Find and classify ALL turning points of y = x⁴ - 8x² + 5 using d²y/dx².

[7 marks]