SOLUTION: Given the following diagram for a continuous function. Answer true or false for the following statements When x = 2, f(x) = 6, f '(x) = 2, f ''(x) = -8 When x = 4, f(x) = 12

Algebra ->  Test  -> Lessons -> SOLUTION: Given the following diagram for a continuous function. Answer true or false for the following statements When x = 2, f(x) = 6, f '(x) = 2, f ''(x) = -8 When x = 4, f(x) = 12      Log On


   

Question 1163582: Given the following diagram for a continuous function. Answer true or false for the following statements
When x = 2, f(x) = 6, f '(x) = 2, f ''(x) = -8
When x = 4, f(x) = 12, f '(x) = 0, f ''(x) = -1
When x = 6, f(x) = 15, f '(x) = 3, f ''(x) = 0
When x = 8, f(x) = 20, f '(x) = 4, f ''(x) = 5
When x = 10, f(x) = 25, f '(x) = 2, f ''(x) = 6
a. 𝑓(𝑥) has a local min at x = 8
b. 𝑓(𝑥) has a local max at x= 4
c. 𝑓(𝑥) has a point of inflection at x = 6
d. 𝑓(𝑥)is increasing on the interval [2, 10]
e. 𝑓(𝑥) has a POI on the interval 6 < x < 10
Determine whether each statement is true or false.
Thank you.
Answer by solver91311(24713) About Me  (Show Source):
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For a local extremum, the first derivative must be zero. For a maximum, the second derivative is negative, for a minimum, the second derivative is positive.

A point of inflection occurs when the second derivative changes sign. So the point must have a zero second derivative and the second derivative on one side needs to be the opposite sign of the second derivative on the other side.

A function is increasing on an interval if the first derivative is positive at every point on the interval. A function is decreasing on an interval if the first derivative is negative at every point on the interval.


John

My calculator said it, I believe it, that settles it