For this week's discussion, you are asked to generate a continuous...

Question
For this week's discussion, you are asked to generate a continuous and differentiable function f (x) with the following properties:
f (x) is decreasing at x = -6
f (x) has a local minimum at x = - 2
f (x) has a local maximum at x - 2
Hints:
Use calculus!
Before specifying a function f (x), first determine requirements for its derivative f ' (x) For example, one of the requirements is that f ' (-2) = 0
If you want to find a function g (x) such that g ( - 9) = 0 and g (8) = 0, , then you could try g (x) = (x + 9) (x - 8).
If you have a possible function for f ' (x), then use the techniques in Indefinite Integrals this Module to try a possible f (x).
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        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        7.89mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        6.97mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
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      • select * from `subjects` where `subjects`.`id` in (6)
        1.22mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
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      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 58049 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.47mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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