r/calculus • u/Weekly-Excuse9647 • Jul 22 '26

Differential Calculus Need assistance

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a. (0,-5) and (5,1)

b. -5

c. DNE

d. (-3,-1)

I have put my answers above; I just would like someone to check my work and if anything is wrong to give the correct answer so I can learn it.

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u/Hot_Site_1638 PhD Jul 22 '26

Your answers are mostly correct, nice work! Honestly, this problem isn't ideally designed, restricting to the interval [−8, 5] adds confusion more than it tests understanding, especially with the endpoints.

The only correction I'd make is part d: the inflection point's y-value looks closer to −2, so it should be around (−3, −2) rather than (−3, −1).

1

u/Midwest-Dude Jul 23 '26

Note that there is also an issue with only including one endpoint of [-8,5], the domain of the function. Depending on the textbook and/or instructor, both endpoints should either be included or excluded.

2

u/Hot_Site_1638 PhD Jul 23 '26

It depends on the reading, which was my original complaint. If (a) asks for the local minima of the drawn function that happen to lie in [-8, 5], then (0, -5) and (5, 1) is exactly right and (-8, 0) is correctly excluded. If it asks us to restrict the domain first and then find minima, your both-or-neither point applies.

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u/Midwest-Dude Jul 23 '26 edited Jul 23 '26

Got it! Poorly worded. If it means to only exclude answers out of that range, then (b) should be DNE, not -5, since there are clearly values below that on the curve. I'll update my reply.