配套习题- 利用导数判断三角函数零点个数 -【青果学院】

1/3单选题

难度：

1.

函数的导函数的最大值等于1，则实数的值为（）

A	2
B	1
C	-1
D	1

正确答案：Qg==

PHA+6Kej77ya5pi+54S2PGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTlptd2EzZjJBQUFCYmxDLV9obzk3Mi5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOWm13YTNmMkFBQUJibEMtX2hvOTcyLnBuZyIgaGVpZ2h0PSIyMSIgd2lkdGg9IjM4Ij7vvIzmiYDku6U8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOWm5Cc0tFcUFBQUI1amV6Mi0wNjQzLnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5abkJzS0VxQUFBQjVqZXoyLTA2NDMucG5nIiBoZWlnaHQ9IjIxIiB3aWR0aD0iNTYiPmNvczxzdXA+Mjwvc3VwPiA8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvRUIvckJBQ0oxVExOWm14d3puWUFBQUJXYWUzMnJVOTc2LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9FQi9yQkFDSjFUTE5abXh3em5ZQUFBQldhZTMyclU5NzYucG5nIiBoZWlnaHQ9IjQzIiB3aWR0aD0iOCI+77yLMTxicj48aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvNzQvMjgvckJBQ0UxVExOWm14cExxY0FBQUJCWk1zSXZ3OTUwLnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC83NC8yOC9yQkFDRTFUTE5abXhwTHFjQUFBQkJaTXNJdnc5NTAucG5nIiBoZWlnaHQ9IjIxIiB3aWR0aD0iMjYiPu+8izxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9FQi9yQkFDSjFUTE5abWljYXVuQUFBQlpCWE00ZE04NTUucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0VCL3JCQUNKMVRMTlptaWNhdW5BQUFCWkJYTTRkTTg1NS5wbmciIGhlaWdodD0iMjEiIHdpZHRoPSI1OSI+Y29zIDxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC9BQi9ENi9yQkFDRkZUTE5acXg1Q0xQQUFBQmxBcGg5cms3NTEucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwL0FCL0Q2L3JCQUNGRlRMTlpxeDVDTFBBQUFCbEFwaDlyazc1MS5wbmciIGhlaWdodD0iMjEiIHdpZHRoPSI1NCI+77yMPGJyPuWboOatpDxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC83NC8yOC9yQkFDRTFUTE5aclI4MHlJQUFBQ0sxRl9GakU2OTAucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzc0LzI4L3JCQUNFMVRMTlpyUjgweUlBQUFDSzFGX0ZqRTY5MC5wbmciIGhlaWdodD0iMjEiIHdpZHRoPSI5MyI+77yM5YW25pyA5aSn5YC85Li6Me+8jOaVheaciTxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC9BQi9ENi9yQkFDRkZUTE5acnhDUF9yQUFBQlltamIyNDg1NTcucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwL0FCL0Q2L3JCQUNGRlRMTlpyeENQX3JBQUFCWW1qYjI0ODU1Ny5wbmciIGhlaWdodD0iMjEiIHdpZHRoPSI1MCI+PC9wPg==

2/3单选题

难度：

2.

下列函数中，在（0，）上有零点的函数是（）

A
B
C
D

正确答案：RA==

PHA+6Kej77ya5a+55LqOQe+8mmYn77yIeO+8iT1jb3N4LTHvvJww77yMeOKIiO+8iDDvvIw8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPu+8iTxicj7iiLRm77yIeO+8ieWcqO+8iDDvvIw8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPu+8ieS4iuWNleiwg+mAkuWHj++8jDxicj48L3A+PHA+5LiUZu+8iDDvvIk9MO+8jOaVheivpeWHveaVsOWcqO+8iDDvvIw8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPu+8ieS4iuaXoOmbtueCue+8jOaVhemUme+8mzxicj7lr7nkuo5C77ya5LukZuKAsu+8iHjvvIk9Y29zeC08aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYV9ETTM1ZEFBQUJtZDZTRmJVNzQxLnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5hX0RNMzVkQUFBQm1kNlNGYlU3NDEucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPj0w77yM5b6XeDxzdWI+MTwvc3ViPj1hcmNjb3M8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYV9ETTM1ZEFBQUJtZDZTRmJVNzQxLnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5hX0RNMzVkQUFBQm1kNlNGYlU3NDEucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPu+8jDxicj7lvZMw77yceO+8nHg8c3ViPjE8L3N1Yj7ml7bvvIxm4oCy77yIeO+8ie+8njDvvIzlvZN4PHN1Yj4xPC9zdWI+77yceO+8nDxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGhlaWdodD0iNDIiIHdpZHRoPSIxNyI+5pe277yMZuKAsu+8iHjvvInvvJww77yMPGJyPuWboOatpGbvvIh477yJ5Zyo77yIMO+8jHg8c3ViPjE8L3N1Yj7vvInkuIrljZXosIPpgJLlop7vvIzlnKjvvIh4PHN1Yj4xPC9zdWI+77yMPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij7vvInkuIrljZXosIPpgJLlh4/vvIw8YnI+6ICMZu+8iDDvvIk9MO+8jGbvvIg8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPu+8iT0w77yM5pWF6K+l5Ye95pWw5Zyo77yIMO+8jDxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGhlaWdodD0iNDIiIHdpZHRoPSIxNyI+77yJ5LiK5peg6Zu254K577yM5pWF6ZSZ77ybPGJyPuWvueS6jkPvvJpm4oCy77yIeO+8iT0yc2lueGNvc3gtMT1zaW4yeC0x4omkMO+8jHjiiIjvvIgw77yMPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij7vvIk8YnI+4oi0Zu+8iHjvvInlnKjvvIgw77yMPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij7vvInkuIrljZXosIPpgJLlh4/vvIzkuJRm77yIMO+8iT0w77yM5pWF6K+l5Ye95pWw5Zyo77yIMO+8jDxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGhlaWdodD0iNDIiIHdpZHRoPSIxNyI+77yJ5LiK5peg6Zu254K577yM5pWF6ZSZ77ybPGJyPuWvueS6jkTvvJrku6Rm4oCy77yIeO+8iT0yc2lueGNvc3gtPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmFfRE0zNWRBQUFCbWQ2U0ZiVTc0MS5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYV9ETTM1ZEFBQUJtZDZTRmJVNzQxLnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij49c2luMngtPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmFfRE0zNWRBQUFCbWQ2U0ZiVTc0MS5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYV9ETTM1ZEFBQUJtZDZTRmJVNzQxLnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij49MO+8jOW+l3g8c3ViPjE8L3N1Yj49YXJjc2luPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmFfRE0zNWRBQUFCbWQ2U0ZiVTc0MS5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYV9ETTM1ZEFBQUJtZDZTRmJVNzQxLnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij7vvIw8YnI+PC9wPjxwPuaIlng8c3ViPjI8L3N1Yj49z4AtYXJjc2luPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmFfRE0zNWRBQUFCbWQ2U0ZiVTc0MS5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYV9ETTM1ZEFBQUJtZDZTRmJVNzQxLnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij7vvIw8YnI+5b2TMO+8nHjvvJx4PHN1Yj4xPC9zdWI+5pe277yMZuKAsu+8iHjvvInvvJww77yM5b2TeDxzdWI+MTwvc3ViPu+8nHjvvJx4PHN1Yj4yPC9zdWI+5pe277yMZuKAsu+8iHjvvInvvJ4w77yM5b2TeDxzdWI+Mjwvc3ViPu+8nHjvvJw8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPuaXtu+8jGbigLLvvIh477yJ77ycMO+8jDxicj7lm6DmraRm77yIeO+8ieWcqO+8iDDvvIx4PHN1Yj4xPC9zdWI+77yJ5LiK5Y2V6LCD6YCS5YeP77yM5Zyo77yIeDxzdWI+MTwvc3ViPu+8jHg8c3ViPjI8L3N1Yj7vvInkuIrljZXosIPpgJLlop7vvIw8YnI+PC9wPjxwPuWcqO+8iHg8c3ViPjI8L3N1Yj7vvIw8aW1nIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgZGF0YS1ja2Utc2F2ZWQtc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBoZWlnaHQ9IjQyIiB3aWR0aD0iMTciPu+8ieS4iuWNleiwg+mAkuWHj++8jDxicj7ogIxm77yIMO+8iT0w77yMZu+8iDxpbWcgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC8zRi9BQy9yQkFDSmxUTE5heUM3NWstQUFBQmpqaUJXczQyOTQucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGhlaWdodD0iNDIiIHdpZHRoPSIxNyI+77yJPTDvvIzmlYXor6Xlh73mlbDlnKjvvIgw77yMPGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzNGL0FDL3JCQUNKbFRMTmF5Qzc1ay1BQUFCamppQldzNDI5NC5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvM0YvQUMvckJBQ0psVExOYXlDNzVrLUFBQUJqamlCV3M0Mjk0LnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjE3Ij7vvInkuIrmnInpm7bngrnvvIzmlYXmraPnoa7vvJs8YnI+5pWF6YCJRO+8jjxicj48L3A+

3/3单选题

难度：

3.

设定义在R上的函数ƒ (x) 是最小正周期为2π的偶函数，ƒ ^′(x) 是ƒ (x) 的导函数．当x∈[0，π]时，0<ƒ (x)<1 ,当x∈(0,π) 且x≠π2 时，（x−π2 ）ƒ ^′(x)>0 ,则函数y=ƒ (x)−sinx 在【−2π，2π】上的零点个数为（）

A	2
B	4
C	5
D	8

正确答案：Qg==

PHA+PGltZyBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzQ4LzMxL3JCQUNKMVRhekdYQlpDX3NBQUNQZzl6ZGVmTTAxNy5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvNDgvMzEvckJBQ0oxVGF6R1hCWkNfc0FBQ1BnOXpkZWZNMDE3LnBuZyIgYWx0PSIiIHN0eWxlPSJ3aWR0aDogNDU3cHg7IGhlaWdodDogNDY3cHg7Ij48L3A+