{"question":{"question":{"content":"**Select all the intervals where $h(x)>0$ and $h'(x)<0$.** [[☃ radio 1]] ![graph](web+graphie://ka-perseus-graphie.s3.amazonaws.com/7e5ba29fbcb033e9b7d7a42e940b3f5ea4272c16) ","images":{"web+graphie://ka-perseus-graphie.s3.amazonaws.com/7e5ba29fbcb033e9b7d7a42e940b3f5ea4272c16":{"width":425,"height":425}},"widgets":{"radio 1":{"type":"radio","alignment":"default","static":false,"graded":true,"options":{"choices":[{"content":"$-4.50$ means $h$ is **positive**, so its graph is above the $x$-axis. $h(x)<0$ means $h$ is **negative**, so its graph is below the $x$-axis. $h'(x)>0$ means $h$ is **increasing**. $h'(x)<0$ means $h$ is **decreasing**. We are asked to find an interval where $h(x)>0$ and $h'(x)<0$, so we need an interval where the graph of $h$ is **above 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 $h(x)>0$ and $h'(x)<0$. ![graph](web+graphie://ka-perseus-graphie.s3.amazonaws.com/c303b1ec0b7511f681113965b3cba7ebeee88fa8)","images":{"web+graphie://ka-perseus-graphie.s3.amazonaws.com/c303b1ec0b7511f681113965b3cba7ebeee88fa8":{"width":425,"height":425}},"widgets":{}},{"replace":false,"content":"Now we can check each option: Interval | | Is $h(x)>0$ and $h'(x)<0$? :-: | :-: | :-: $-4.5

Derivative & the direction of a function

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