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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
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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

 

cool cool cool

CPhill  May 24, 2017
edited by CPhill  May 24, 2017

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