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For this problem, consider the function y=f(x)= (a) The y intercept is the point

ID: 2889605 • Letter: F

Question

For this problem, consider the function

y=f(x)=


(a) The y intercept is the point (

,

).

(b) The only x intercept is at x=

.

(c) The left-most vertical asymptote has equation x=

.

(d) The right-most vertical asymptote has equation x=

.

(e) What is the formula for f'(x)=



(f) How many critical numbers are there for f(x)?



(g) There are three critical numbers c having the property that f'(c)=0; list these in increasing order:



(h) The open intervals on which f(x) is increasing. (Enter the interval that contains smaller numbers first. If you need to use - or , enter -infinity or infinity.)(

,

)
(

,

)

(i) The open intervals on which f(x) is decreasing. (Enter the interval that contains smaller numbers first. (If you need to use - or , enter -infinity or infinity.)(

,

)
(

,

)
(

,

)

(j) There is a local maximum occurring at c=

.

(j) There is a local minimum occurring at c=

.

(k) The formula for f''(x)=



(l) The open intervals on which f(x) is concave up. (Enter the interval that contains smaller numbers first. (If you need to use - or , enter -infinity or infinity.)(

,

)
(

,

)

(m) The open intervals on which f(x) is concave down. (Enter the interval that contains smaller numbers first. If you need to use - or , enter -infinity or infinity.)(

,

)
(

,

)
(n) T or F: There is an inflection point at (-3,f(-3))

TrueFalse    

.
(o) T or F: There is an inflection point at (0,f(0))

TrueFalse    

.
(p) T or F: There is an inflection point at (3,f(3))

TrueFalse    

.
(q) The graph of y=f(x) is best represented by which of the following pictures (select A, B, C or D):

AB    CD

x3 x2 – 1

Explanation / Answer

y=f(x)=x 3/(x 2-1)

a. y intercept means x=0

f(0)=0/(0-1)=0

y intercept (0,0)

b. x intercept

f(x)=0

0=x 3

x=0

x intercept (0,0)

c. vertical asymptote x 2-1=0

x=-1,1

left vertical asymptote,x=-1

d. right vertical asymptote, x=1

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