use the graph of ( y = f(x) ), assuming ( f^{prime prime}(x)<0 ) if ( x = f ), to answer parts (a) through…

use the graph of ( y = f(x) ), assuming ( f^{prime prime}(x)<0 ) if ( x = f ), to answer parts (a) through (f).\n(a) identify intervals on which the graph of ( f ) is concave upward. choose the correct answer below.\n( \bigcirc ) a. ( (b, c),(c, e),(g, h) )\n( \bigcirc ) b. ( (a, b),(d, e),(g, h) )\n( \bigcirc ) c. ( (a, c),(c, d),(e, g) )\n( \bigcirc ) d. ( (d, e),(g, h) )\n( \bigcirc ) e. ( (e, g) )\n( \bigcirc ) f. ( (a, c),(c, e),(g, h) )\n( \bigcirc ) g. the graph is never concave upward.\n(b) identify intervals on which the graph of ( f ) is concave downward. choose the correct answer below.\n( \bigcirc ) a. ( (b, c),(c, e),(g, h) )\n( \bigcirc ) b. ( (e, g) )\n( \bigcirc ) c. ( (b, c),(c, d),(e, g) )\n( \bigcirc ) d. ( (a, c),(c, e),(g, h) )\n( \bigcirc ) h. ( (a, b),(e, g) )

use the graph of ( y = f(x) ), assuming ( f^{prime prime}(x)<0 ) if ( x = f ), to answer parts (a) through (f).\n(a) identify intervals on which the graph of ( f ) is concave upward. choose the correct answer below.\n( \bigcirc ) a. ( (b, c),(c, e),(g, h) )\n( \bigcirc ) b. ( (a, b),(d, e),(g, h) )\n( \bigcirc ) c. ( (a, c),(c, d),(e, g) )\n( \bigcirc ) d. ( (d, e),(g, h) )\n( \bigcirc ) e. ( (e, g) )\n( \bigcirc ) f. ( (a, c),(c, e),(g, h) )\n( \bigcirc ) g. the graph is never concave upward.\n(b) identify intervals on which the graph of ( f ) is concave downward. choose the correct answer below.\n( \bigcirc ) a. ( (b, c),(c, e),(g, h) )\n( \bigcirc ) b. ( (e, g) )\n( \bigcirc ) c. ( (b, c),(c, d),(e, g) )\n( \bigcirc ) d. ( (a, c),(c, e),(g, h) )\n( \bigcirc ) h. ( (a, b),(e, g) )

Answer

Explanation:

Step1: Recall concavity rules

If (f''(x)>0), the graph is concave upward. If (f''(x)<0), the graph is concave downward.

Step2: Analyze the graph

Looking at the graph, the intervals where the graph is concave upward are ((a,c)), ((c,e)), ((g,h))

Answer:

A. ((b,c),(c,e),(g,h)) is incorrect. B. ((a,b),(d,e),(g,h)) is incorrect. C. ((a,c),(c,d),(e,g)) is incorrect. D. ((a,c),(c,e),(g,h)) is correct. E. ((e,g)) is incorrect. F. ((a,c),(c,e),(g,h)) is correct. G. The graph is never concave upward is incorrect. H. ((a,b),(e,g)) is incorrect.

So the answer is D. ((a,c),(c,e),(g,h))