Estimate the x-values of critical points of f(x) on the interval 0

f(0)>f(1) and f(1)<f(2), therefore a critical point exists at f(1). As the value is greater before the critical point and is greater after as well, thus there exists a local minima at x=1.

f(3) <f(4) and f(4)>f(5), therefore a critical point exists at f(4). As the value is less before the critical point and is less after as well, thus there exists a local maxima at x=4.

Step-by-step explanation:

As the data table is missing in the question, a similar question is found, which is as attached here with.

From the data of table

x           | 0  | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  |

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y=f(x)    | -3 | -5 | -4 | -1 | 2  | 1  | -1  | -3 | -4 | -6 | -7 |

From the graph attached the critical points are as given below

As

f(0)>f(1) and f(1)<f(2), therefore a critical point exists at f(1). As the value is greater before the critical point and is greater after as well, thus there exists a local minima at x=1.

f(3) <f(4) and f(4)>f(5), therefore a critical point exists at f(4). As the value is less before the critical point and is less after as well, thus there exists a local maxima at x=4.