Question

use the graph of f to complete the following table. x f(x) f ′(x) x > 0 f(x) > 0 f ′(x) ? 0 x > 0 f(x) < 0 f ′(x) ? 0 x < 0 f(x) > 0 f ′(x) ? 0 x < 0 f(x) < 0 f ′(x) ? 0

Answer 1

To complete the table, we need to determine the signs of f(x) and f'(x) for different values of x. The graph provided helps us determine that for x > 0, f(x) > 0 and f'(x) = 0, while for x < 0, f(x) < 0 and f'(x) = 0.

Step-by-step explanation:

To complete the table, we need to determine the signs of f(x) and f'(x) for different values of x. Looking at the given graph of f(x), we can see that for x > 0, f(x) is positive and f'(x) is zero. This means that for x > 0, f(x) > 0 and f'(x) = 0.

On the other hand, for x < 0, f(x) is negative and f'(x) is also zero. Therefore, for x < 0, f(x) < 0 and f'(x) = 0.

Based on the information from the graph, we can now complete the table:

xf(x)f'(x)x > 0f(x) > 0f'(x) = 0x > 0f(x) < 0f'(x) = 0x < 0f(x) > 0f'(x) = 0x < 0f(x) < 0f'(x) = 0