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.Com
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) (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS
Let f be a continuous function such that f(-1) = -1 and f(1) = 1.
Classify each of the... (answered by robertb)
Let f be a continuous function such that f(-1) = -1 and f(1) = 1.
Classify each of the... (answered by richard1234)
HELP:
Given 2 functions f(x)-2x-5 and g(x)=x^2. Determine whether each of the following... (answered by CharlesG2,rapaljer)
Given 2 functions f(x)=2x-5 and g(x) =x^2.
Determine whether each of the following... (answered by stanbon)
For the following trigonometric function, identify whether the identity stated is true or (answered by Theo)
Given two functions f(x)=2x-5 and g(x)=x^2. Are the following statements true or false... (answered by Fombitz)
Given two functions f(x)=2x-5 and g(x)=x^2. Are the following statements true or false.... (answered by CharlesG2)
The function f(x)= sqrt(sin(x)(sin(x) -2)+1) is continuous at x = pi/2. ( true or... (answered by ikleyn)
Answer the following questions for a continuous random variable X with density function... (answered by Boreal)