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![A function
f is continuous on the closed interval
[4,6] and twice differentiable on the open interval
(4,6). If
f^(')(5)=-3, and
f is concave downwards on the given interval, which of the following could be a table of values for
f ?
(A)
x
f(x)
4
8
(B)
x
f(x)
4
8](https://blblobstorage.blob.core.windows.net/solver-b2c/118ea8ac-011e-11ef-9921-fae99310ca6d.jpg)
. A function is continuous on the closed interval and twice differentiable on the open interval . If , and is concave downwards on the given interval, which of the following could be a table of values for ?(A)\begin{tabular}{|c|c|}\hline & \\\hline & \\\hline\end{tabular}(B)\begin{tabular}{|c|c|}\hline & \\\hline & \\\hline\end{tabular}
Full solution
Q. . A function is continuous on the closed interval and twice differentiable on the open interval . If , and is concave downwards on the given interval, which of the following could be a table of values for ?(A)\begin{tabular}{|c|c|}\hline & \\\hline & \\\hline\end{tabular}(B)\begin{tabular}{|c|c|}\hline & \\\hline & \\\hline\end{tabular}
- Check Derivative at : : Check the derivative at for both tables.For table (A), we need to find the slope between the points and . Since we don't have , we can't find the slope.
- Check Concavity for Table (A): : Check the concavity of the function for table (A). Since the function is concave downwards, should be negative. Without additional points, we can't determine the concavity from table (A).
- Check Derivative at : : Check the derivative at for table (B). Again, we need to find the slope between the points and . Since we don't have , we can't find the slope.
- Check Concavity for Table (B): : Check the concavity of the function for table (B). Without additional points, we can't determine the concavity from table (B).
- Realize Mistake: : Realize that we made a mistake; we can't determine the slope at without the value of for either table.
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