Question

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

x f(x)
-4 -6
-3 -4
-2 -1
-1 -2
0 -5
1 -8
2 -16
a) (-3,-4)
b) (-2,-1)
c) (0,-5)
d) (1,-5)

Answer 1

Option (b) (-2, -1) is the possible turning point for the continuous function f(x), as it is the point where the function changes from increasing to decreasing.

Step-by-step explanation:

Identifying a Turning Point of a Continuous Function

To find a possible turning point for the continuous function f(x), we need to consider the points provided and determine where there is a change in the direction of the function. A turning point is where the function changes from increasing to decreasing (a relative maximum) or from decreasing to increasing (a relative minimum). We analyze the given points and look for a change in the f(x) values as x increases.

1. (-4, -6): Decreasing
2. (-3, -4): Increasing
3. (-2, -1): Increasing
4. (-1, -2): Decreasing
5. (0, -5): Decreasing
6. (1, -8): Decreasing

Between (-3,-4) and (-2,-1), the function is moving upwards (increasing), and then between (-2,-1) and (-1,-2), it starts to decrease. This indicates that there is a turning point between (-2,-1) and (-1,-2). Thus, option (b) (-2,-1) is a possible turning point for the function f(x).