will rate lifesaver Find the local maximum and minimum values of f using both th

Question

will rate lifesaver

Find the local maximum and minimum values of f using both the First and Second Derivative Tests. f(x) = 5 + 9x2 - 6x3 local maximum value local minimum value This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Suppose f " is continuous on (-infinity, infinity). If f '(2) = 0 and f "(2) = 6, what can you say about f ?

Explanation / Answer

f ' (x) = 18x - 18x^2

f " (x) = 18 - 36x

f ' (x) = 0 means 18x(1 - x) = 0

so x = 0 or 1

at x = 0 , f " (x) = 18 positive so at x = 0 it is minimum

at x = 1 , f " (x) = -18 means negative so at x = 1 it is maximum

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

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