Question

Which is a possible turning point for the continuous function f(x)

Answer 1

(-2, -1)

Step-by-step explanation:

In calculus, if a function is differentiable and of one variable, then a turning point of this function is a point on the graph where the function's derivative is zero. that is, the function stops increasing or decreasing. Since we know that the function of the graph is continuous, then (-2, -1) is the most likely turning point because at this point the function stops increasing and starts decreasing. All points have been plotted below. The turning point is in blue.

Answer 2

Answer: Choice B (-2,-1)

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Step-by-step explanation:

I recommend plotting the points shown in the table. Each point is in the form (x,y) where y = f(x).

The points to be plotted are:
(-4,-6)
(-3,-4)
(-2,-1)
(-1,-2)
(0,-5)
(1,-8)
(2,-16)

Based on the graph (see attached), we see that the point (-2,-1) is the most likely turning point. This point is shown in red. This is where the graph is most likely to change from increasing to decreasing. Though other scenarios are possible.

Note: it's not guaranteed that (-2,-1) is the actual turning point because we don't have enough info about this function.

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If you are not allowed to graph, then I recommend looking at the y coordinates. Note how y increases for the first three points (-6, -4, -1), but then it decreases after it reaches y = -1. So this helps confirm that (-2,-1) is the answer