Properties of the First Derivative from Data

Question

The table below shows selected values for a function $$f$$.

| $$ x $$ | 1 | 2 | 3 | 4 | 5 |
|------|---|---|---|---|---|
| $$ f(x) $$ | 9 | 4 | 0 | -3 | -5 |

Given that $$f$$ is twice-differentiable on the interval $$ 1 \leq x \leq 5 $$, which of the following statements could be true?

Accepted Answer

$$ f' $$ is negative and increasing for $$ 1 \leq x \leq 5 $$

Answer

$$ f' $$ is negative and decreasing for $$ 1 \leq x \leq 5 $$

Answer

$$ f' $$ is positive and increasing for $$ 1 \leq x \leq 5 $$

Answer

$$ f' $$ is positive and decreasing for $$ 1 \leq x \leq 5 $$

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