Question

Graph the function y = x3 + 6x2 + 2x – 11. Based on the graph, what is the largest possible x-value if y = 0? Round your answer to the nearest hundredth, if necessary.?

Answer 1

Answer:

The answer to this question corresponds to computing the largest root of our function. Due to the way in which the question is asked, we can have 2 answers based on the root criteria. Please, read on for the explanation.

Step-by-step explanation:

First, to graph the function we can use any graphing tool available, for this case we chose the free online tool called Desmos calculator. Attached is a graph of the function.

Desmos calculator already shows as the position of the 3 roots. Roots are points on a function whose y-component is zero, meaning the points where the function crosses the x axis.

From the graph we can see that these points are $x= -5.211$, $x= -1.9$ and $x= 1.111$.

The ambiguity of the answer comes in choosing the root either with the most positive value, or the root with the largest magnitude. From the way in which the question is asked, we could understand both of these cases.

In case the root with most positive value is asked, then the answer is $x= 1.111$. However, in case the root with largest magnitude is asked, then the answer is $x= -5.211$.

As a reference, you can have a look at the following links:

https://en.wikipedia.org/wiki/Magnitude_(mathematics)

https://en.wikipedia.org/wiki/Cubic_function

Answer 2

Answer:

The highest value of x is 1.11 when y = 0.

Step-by-step explanation:

We are given the following information in the question:

$y = x^3 + 6x^2 + 2x -11$

The attached image shows the graph for given function.

The graph shows all the possible values of x when y = 0.

(-5.211,0)

(-1.9,0)

(1.111,0)

So the highest value of x is 1.11 when y = 0.