{"question":{"question":{"content":"**Select all the intervals where $f(x)<0$ and $f'(x)>0$.** [[☃ radio 1]] ![graph](web+graphie://ka-perseus-graphie.s3.amazonaws.com/d3ae97edd07fd1c3f30d1809fafd26d770e958e0) ","images":{"web+graphie://ka-perseus-graphie.s3.amazonaws.com/d3ae97edd07fd1c3f30d1809fafd26d770e958e0":{"width":425,"height":425}},"widgets":{"radio 1":{"type":"radio","alignment":"default","static":false,"graded":true,"options":{"choices":[{"content":"$-10$ means $f$ is **positive**, so its graph is above the $x$-axis. $f(x)<0$ means $f$ is **negative**, so its graph is below the $x$-axis. $f'(x)>0$ means $f$ is **increasing**. $f'(x)<0$ means $f$ is **decreasing**. We are asked to find an interval where $f(x)<0$ and $f'(x)>0$, so we need an interval where the graph of $f$ is **below the $x$-axis and increasing**.","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 $f(x)<0$ and $f'(x)>0$. ![graph](web+graphie://ka-perseus-graphie.s3.amazonaws.com/9051dfa26c24e5155444144502c050b0d6c7dac6)","images":{"web+graphie://ka-perseus-graphie.s3.amazonaws.com/9051dfa26c24e5155444144502c050b0d6c7dac6":{"width":425,"height":425}},"widgets":{}},{"replace":false,"content":"Now we can check each option: Interval | | Is $f(x)<0$ and $f'(x)>0$? :-: | :-: | :-: $-1

Derivative & the direction of a function