Question

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 16, negative 1, 2, negative 1, negative 4, negative 1.
Analyze the table of values for the continuous function, f(x), to complete the statements.

A local maximum occurs over the interval
.

A local minimum occurs over the interval
.

Answer 1

A local maximum occurs over the interval (-2, 0).

A local minimum occurs over the interval (0, 2).

Reason: f(-1)=2 > f(-2) and f(0), so the peak is at x=-1 (between -2 and 0). f(1)=-4 < f(0) and f(2), so the valley is at x=1 (between 0 and 2).