A)State an interval in which the x -coordinate of the maximum turning point on the graph of y=−x(x+2)(x−3) must lie.

B)Use a numerical method to zoom in on this interval and hence estimate the position of the maximum turning point of the graph with the x -coordinate correct to 1 decimal place.

AsadRehman
May 23, 2017

#1**+2 **

y = -x ( x + 2) (x - 3)

The zeroes are at x = -2, x = 0 and x = 3

From (-inf, -2) the graph will be > 0

From (-2, 0) the graph will be < 0

From (0, 3) the graph will be > 0

And from (3, inf) the graph will be < 0

A minimum turning point will occur on ( -2, 0) and a maximum turning point will occur between (0, 3)

We could use Calculus to find these turning points but look at the graph here : https://www.desmos.com/calculator/1qkjsbo1r3

It shows that the max turning point occurs at x ≈ 1.786 ≈ 1.8

CPhill
May 24, 2017