1. **Stating the problem:** We analyze the curve of $\hat{f}$ and determine which of the given statements about the function $f$ are correct or incorrect. 2. **Understanding the relationship between $\hat{f}$ and $f$:** The curve $\hat{f}$ is the opposite figure of $f$, which means $\hat{f}(x) = -f(x)$. 3. **Analyzing statement (a):** "At $x = -5$ there is a maximum local value of $f$." - Since $\hat{f}$ has a peak (maximum) at $x = -5$, $f(x) = -\hat{f}(x)$ will have a minimum at $x = -5$ (because the sign is reversed). - Therefore, statement (a) is **incorrect**. 4. **Analyzing statement (b):** "$f''(1) > 0$." - $\hat{f}$ has a minimum near $x=1$, so $\hat{f}''(1) > 0$ (concave up). - Since $f(x) = -\hat{f}(x)$, then $f''(x) = -\hat{f}''(x)$. - Thus, $f''(1) = -\hat{f}''(1) < 0$, so statement (b) is **incorrect**. 5. **Analyzing statement (c):** "At $x = 7$ there is a minimum local value of $f$." - $\hat{f}$ has a maximum near $x=7$, so $f$ has a minimum at $x=7$ (sign reversed). - Statement (c) is **correct**. 6. **Analyzing statement (d):** "The function $f$ is decreasing on $] -5,1[$." - $\hat{f}$ decreases from $x=-5$ to $x=1$ (from max to min). - Since $f = -\hat{f}$, $f$ increases on $]-5,1[$. - Statement (d) is **incorrect**. 7. **Summary:** The only correct statement is (c). The question asks for the incorrect statements, so all except (c) are incorrect. **Final answer:** The statements (a), (b), and (d) are incorrect; only (c) is correct.