Suppose f \'\' is continuous on (??, ?). (a) If f \' (?5) = 0 and f \'\' (?5) =
ID: 2837507 • Letter: S
Question
Suppose f '' is continuous on (??, ?).
(a) If f '(?5) = 0 and f ''(?5) = 9, what can you say about f ?
1. At x = ?5, f has a local maximum.
2. At x = ?5, f has a local minimum.
3. At x = ?5, f has neither a maximum nor a minimum.
4. More information is needed to determine if f has a maximum or minimum at x = ?5.
(b) If f '(4) = 0 and f ''(4) = 0, what can you say about f ?
1. At x = 4, f has a local maximum.
2. At x = 4, f has a local minimum.
3. At x = 4, f has neither a maximum nor a minimum.
4. More information is needed to determine if f has a maximum or minimum at x = 4.
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Find the critical numbers of the function f(x) = x8(x ? 2)7.
(b) What does the Second Derivative Test tell you about the behavior of f at these critical numbers?
At x = _____, the function has _______.
(c) What does the First Derivative Test tell you that the Second Derivative test does not? (Enter your answers from smallest to largest x value.)
At x = ____, the function has ___________.
x = ? (smallest value) x = ? x =? (largest value)Explanation / Answer
(a) option 2. At x = ?5, f has a local minimum.
(b) option 3. At x = 4, f has neither a maximum nor a minimum.
x =0(smallest value)
x = 16/15
x =2(largest value)
At x = 0, the function has neither maximum nor minimum.
At x = 16/15, the function has local minimum.
At x = 2, the function has neither maximum nor minimum.
At x =0, the function has critical point and slope=0.
At x =16/15, the function has criticalpoint and slope=0.
At x =2, the function has criticalpoin and slope=0t.