hard methods question(HELP)

[tolga]

Q) A proposed sextion of a ride at an amusement park is to be modelled on the curve y=1/500(600x+25x^2-x^3),where y is the height in (m) of the ride above the ground level and x is the horizontal distance(in metres). The x-axis represents ground level. It will travel through a tunnel from A to C;B is the lowest point in the tunnel and D is the highest point in the tunnel and D is the highest point on the ride.
C:\Users\tolga\Pictures\Graph.jpg
a)Find the horizontal distance from A to E.
b)Find the greatest depth below the ground level and the maximum height above ground level that the rollercoaster will reach in this section(correct to 2 decimal places)
c)Describe the impact that a dilation by a factor greater than 1 from the x-axis would have on:
i)the maximum depth and maximum height from b
ii)the point at which the rollercoaster would emerge from the tunnel.
iii)the gradient of the slope at this point.

[superflya]

differentiate and equate dy/dx=0 to find max and min points.

[tolga]

How exactly do we do that can you show working out

[superflya]

use quadratic formula or calc to solve

[tolga]

what about the horizontal sdistance

[the.watchman]

Factorise the equation to get the x-intercepts (one of them is zero)
Then, with the other two, find their values, and thus their distance

[Blakhitman]

use quadratic formula or calc to solve

that's 1 mark lost :p twooo decimal places.

For the horizontal distance, wouldn't you just find the x-intercepts?

[tolga]

what about part c

[andy456]

You just have to apply the theories of dilation to the graph.....