+476 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.
+128407
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
