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 – 1Explanation / 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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