We are finding intervals of concavity of f(x) = x4 - 4x3 - 18x2 The possible inf

Question

We are finding intervals of concavity of f(x) = x4 - 4x3 - 18x2



The possible inflection point list is {-1,3}


Finally, determine the concavity in each interval between possible inflection points. In each interval, choose a test point and determine whether the second derivative of f is positive or negative throughout the interval.
Remember, we know f ''(x) = 12x2 - 24x - 36.


Interval Test point a Test f ''(a) Concavity
(- infinity,-1) f '' > 0, so f conc up
f '' < 0, so f conc down

(-1,3) f '' > 0, so f conc up
f '' < 0, so f conc down

(3, infinity) f '' > 0, so f conc up
f '' < 0, so f conc down

Explanation / Answer

You may choose any points in the ranges I would suggest round easy one such as -2 for the first interval 0 for the second and 4 for the third.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.