The vertical profile of a section of a roller coaster track is modelled by the curve with equation $y = 2x^3 - 24x$ , where $y$ is the vertical displacement in decametres and $x$ is the horizontal distance in decametres from a support pylon.

Point $A$ on the track is located at horizontal distance $x = 2$ .

Point $B$ on the track is located at horizontal distance $x = 2 + h$ .

Show that the gradient of the chord $A B$ is given by $2h^2 + 12h$ .

Explain how the result of part (a) can be used to show that $A$ is a stationary point on the track section.

Point $A$ on the track is located at horizontal distance $x = 2$ .

Point $B$ on the track is located at horizontal distance $x = 2 + h$ .

Show that the gradient of the chord $A B$ is given by $2h^2 + 12h$ .

Explain how the result of part (a) can be used to show that $A$ is a stationary point on the track section.

1.6 Differentiation

Question 75

Markscheme

1.6 Differentiation

Question 75

Markscheme

1.6 Differentiation

Question 75

1.6 Differentiation Questions

1.6 Differentiation

Question 75

1.6 Differentiation Questions