添加关联题目20496->22764

题库0.3/Problems.json

@@ -539635,7 +539635,9 @@
             "20221230\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022764"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -601718,6 +601720,111 @@
         "space": "4em",
         "unrelated": []
     },
+    "022760": {
+        "id": "022760",
+        "content": "已知$a,b,c$为常数, $a>0$. 证明: 函数$y=ax^2+bx+c$在区间$(-\\infty,-\\dfrac{b}{2a}]$上是严格减函数, 在$[-\\dfrac{b}{2a},+\\infty)$上是严格增函数.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231113\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022761": {
+        "id": "022761",
+        "content": "证明: 函数$y=x+\\dfrac{1}{x}$在区间$(0,1]$上是严格减函数.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231113\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022762": {
+        "id": "022762",
+        "content": "证明: 函数$y=2^{3-2x}$在定义域上是严格减函数.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231113\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022763": {
+        "id": "022763",
+        "content": "写出下列函数的最大值与最小值(若不存在, 就写``不存在''), 并写出取最值时相应自变量的值:\\\\\n(1) $y=x^2-4x-2$: \\blank{150};\\\\\n(2) $y=6x-3x^2$: \\blank{150};\\\\\n(3) $y=-x^2-4x-3$, $x\\in [-3,1]$: \\blank{150};\\\\\n(4) $y=x^2-2x-3$, $x\\in [-2,0]$: \\blank{150}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231113\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022764": {
+        "id": "022764",
+        "content": "函数$f(x)=x+8-\\dfrac ax$在$[1,+\\infty)$上是增函数, 求$a$的取值范围.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一校本作业必修第四章-20231113修改",
+        "edit": [
+            "20221230\t王伟叶",
+            "20231113\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020496"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",