Question

Suppose $f''(x)$ is continuous for all $x$, and the graph of $y = f(x)$ has an inflection point at $x = 9$. Complete the following table with appropriate possibilities for the values of $f''(x)$ at $x = 4, 9, 14..$ egin{array}{|c|c|c|c|} hline x & 4 & 9 & 14 \ hline f''(x) & 0 & 0 & 0 \ hline end{array} Based on your table, the graph of $y = f(x)$ is concave up until $x = 9$, and is concave down after. The graph of $y = f(x)$ will have a local minimum at $x = 9.$

          Suppose $f''(x)$ is continuous for all $x$, and the graph of $y = f(x)$ has an inflection point at $x = 9$.
Complete the following table with appropriate possibilities for the values of $f''(x)$ at $x = 4, 9, 14..$
egin{array}{|c|c|c|c|}
hline
x & 4 & 9 & 14 \
hline
f''(x) & 0 & 0 & 0 \
hline
end{array}
Based on your table, the graph of $y = f(x)$ is concave up until $x = 9$, and is concave down after.
The graph of $y = f(x)$ will have a local minimum at $x = 9.$

Suppose f”(x) is continuous for all x, and the graph of y = f(x) has an inflection point at x = 9.
Complete the following table with appropriate possibilities for the values of f”(x) at x = 4, 9, 14..
eginarray|c|c|c|c|
hline
x 4 9 14 hline
f”(x) 0 0 0 hline
endarray
Based on your table, the graph of y = f(x) is concave up until x = 9, and is concave down after.
The graph of y = f(x) will have a local minimum at x = 9.

Added by Jeremy A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/02/2023

Step 1

B: Show more…

Show all steps

Thanks for your feedback!

Suppose f''(x) is continuous for all x, and the graph of y = f(x) has an inflection point at x = 9. Complete the following table with appropriate possibilities for the values of f''(x) at x = 4, 9, 14. Based on your table, the graph of y = f(x) is concave up until x = 9, and is concave down after. The graph of y = f(x) will have a local minimum at x = 9.