summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y =…
summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). a. f is concave upward on (-∞, 3/2),(3,∞) and concave downward on (3/2,3) b. f is never concave downward; f is concave upward on c. f is never concave upward; f is concave downward on sketch the graph of y = f(x). choose the correct graph below. a. b. c. d.
Answer
Explanation:
Step1: Analyze concavity intervals
We are given that (f) is concave - upward on ((-\infty,\frac{3}{2}),(3,\infty)) and concave - downward on ((\frac{3}{2},3)). A function that is concave - upward has a second - derivative (f''>0) and is concave - downward when (f'' < 0).
Step2: Match with graph
A graph that is concave - upward will open upwards like a cup and a graph that is concave - downward will open downwards like an inverted cup. - Option A: Does not match the given concavity intervals. - Option B: Does not match the given concavity intervals as it does not show the correct change in concavity. - Option C: Does not match the given concavity intervals as it does not show the correct change in concavity. - Option D: Matches the given concavity intervals where the graph is concave - upward on ((-\infty,\frac{3}{2})) and ((3,\infty)) and concave - downward on ((\frac{3}{2},3))
Answer:
D.