{"question":{"question":{"content":"**Select all the intervals where $g(x)<0$ and $g'(x)<0$.** [[☃ radio 1]] ![](web+graphie://ka-perseus-graphie.s3.amazonaws.com/d1a128e46f178cbf3e9c2fa886be7c973ffa2256) ","images":{"web+graphie://ka-perseus-graphie.s3.amazonaws.com/d1a128e46f178cbf3e9c2fa886be7c973ffa2256":{"width":425,"height":425}},"widgets":{"radio 1":{"type":"radio","alignment":"default","static":false,"graded":true,"options":{"choices":[{"content":"$-40$ means $g$ is **positive**, so its graph is above the $x$-axis. $g(x)<0$ means $g$ is **negative**, so its graph is below the $x$-axis. $g'(x)>0$ means $g$ is **increasing**. $g'(x)<0$ means $g$ is **decreasing**. We are asked to find an interval where $g(x)<0$ and $g'(x)<0$, so we need an interval where the graph of $g$ is **below the $x$-axis and decreasing**.","images":{"web+graphie://ka-perseus-graphie.s3.amazonaws.com/2bba5829a68cd57e9ab7140d72123e4cf5de8167":{"width":100,"height":100},"web+graphie://ka-perseus-graphie.s3.amazonaws.com/bce90186c8a7edb6742bd7a86f2eb4568ee3f687":{"width":100,"height":100},"web+graphie://ka-perseus-graphie.s3.amazonaws.com/7f51973e51b0b7cd3176c4ccb2e9cb20b5c51a08":{"width":100,"height":100},"web+graphie://ka-perseus-graphie.s3.amazonaws.com/fad1dc95cd761b6e7f4c581c7093841fcf16029a":{"width":100,"height":100},"web+graphie://ka-perseus-graphie.s3.amazonaws.com/ec6d71e19611a339af32829c9b82bc83d7731795":{"width":100,"height":100}},"widgets":{}},{"replace":false,"content":"Visually, this is where $g(x)<0$ and $g'(x)<0$. ![](web+graphie://ka-perseus-graphie.s3.amazonaws.com/d83768b6238f1df2e3924813a008ebc9a8216be1)","images":{"web+graphie://ka-perseus-graphie.s3.amazonaws.com/d83768b6238f1df2e3924813a008ebc9a8216be1":{"width":425,"height":425}},"widgets":{}},{"replace":false,"content":"Now we can check each option: Interval | | Is $g(x)<0$ and $g'(x)<0$? :-: | :-: | :-: $-40$. $0

Derivative & the direction of a function