Question

suppose that (f(x)) is a function that exists everywhere. suppose we also know that

(f(1) = 0)
(f(2) = 0)
(f(3) = 0)

and

(f(x) < 0) on ((-\infty, 1))

and

(f(x) > 0) on ((1, 2), (2, 3), (3, \infty)).

what are the critical numbers?
(x = \\)

at which critical numbers will we find a local maximum? if there are no local maxima, enter \dne\.
(x = \\)

at which critical numbers will we find a local minimum? if there are no local minima, enter \dne\.
(x = \\)

Explanation:

Identify critical numbers

Using the Critical Points knowledge point

$$
LATEXBLOCK0
$$

Analyze local maxima

Using the Local Extrema and Increasing and Decreasing Intervals knowledge points

$$
LATEXBLOCK1
$$

Analyze local minima

Using the Local Extrema and Increasing and Decreasing Intervals knowledge points

$$
LATEXBLOCK2
$$

Answer:

Question 1

\(x = 1, 2, 3\)

Question 2

\(x = \text{DNE}\)

Question 3

\(x = 1\)