4) If f and g are both decreasing on (a,b) then fg must be decreasing on (a,b) 5) If the graph of f is concave upward on (a,b), then the graph of -f is concave downward on (a,b) 6) If the second derivative of f exists on (a,b) and the graph of f has an inflection point at (c, f(c)) where a
4) If f and g are both decreasing on (a,b) then fg must be decreasing on (a,b) 5) If the graph of f is concave upward on (a,b), then the graph of -f is concave downward on (a,b) 6) If the second derivative of f exists on (a,b) and the graph of f has an inflection point at (c, f(c)) where a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer True or False for questions 4,10, and 11 thank you!!
![True/False
1)
If f is decreasing on (a,b) then f'(x) <0 for each x in (a,b)
2) If f'(c)=0 then f has a relative minimum or a relative maximum at x = c
3) Iff and g are both increasing on (a,b) then f+g is increasing on (a,b)
) If ƒ and g are both decreasing on (a,b) then fg must be decreasing on (a,b)
5)
If the graph of f is concave upward on (a,b), then the graph of -f is concave downward
on (a,b)
6) If the second derivative of f exists on (a,b) and the graph of f has an inflection point at
(c, f(c)) where a <c<b, then fƒ"(c)=0
7) If c is a critical number of f where a <c<band f"(c) <0 on (a,b), then f has a relative
minimum at x = c
8)
The graph of a function f(x) cannot intersect its vertical asymptote.
9) The graph of a function f(x) cannot intersect its horizontal asymptote.
10) If f(x) is not continuous on the interval [a,b] then f(x) cannot have an absolute maximum
value.
11) If f(x) is defined on a closed interval [a,b] then f(x) has an absolute minimum value.
12) If f(x) is continuous on [a,b], f(x) is differentiable on (a,b), and f'(x) #0 for all x in (a,b),
then the absolute maximum value of f(x) on [a,b] is f(a) or f(b).
13) If x <y, then e* <e"
14) If 0<b<1 and x<y, then b* >b²
15) If e** >0 then k>0 and x>0.
16) f(x) = ex is an increasing function if k>0 and a decreasing function if k<0.
17) (In x³)=3 lnx for all x in (0,00)
18) If a>0 and b>0 then In(a+b) = ln a + ln b
19) If b>0, then enb= ln e
20) If f(x)=3" then f'(x) = x3-¹
21) If f(x) = e²
then f'(x) = e
22) If ƒ(x) = π*
then f'(x) = n*
23) If f(x)=e³x² then f'(x) = ex
1
24) f(x) = ln |x| then f'(x):
25) f(x) = ln 5 then f'(x) =
P
26) f(x) = ln(x+5)² then f'(x) =
x
1
(x + 5)²
27) If you are modeling exponential decay, you can use a model of the form Q(t)=Qe](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6f420b8-13d1-4377-8749-654e8013e456%2F1d69c48f-1244-42e1-8348-c621939de427%2F1ejn2kh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:True/False
1)
If f is decreasing on (a,b) then f'(x) <0 for each x in (a,b)
2) If f'(c)=0 then f has a relative minimum or a relative maximum at x = c
3) Iff and g are both increasing on (a,b) then f+g is increasing on (a,b)
) If ƒ and g are both decreasing on (a,b) then fg must be decreasing on (a,b)
5)
If the graph of f is concave upward on (a,b), then the graph of -f is concave downward
on (a,b)
6) If the second derivative of f exists on (a,b) and the graph of f has an inflection point at
(c, f(c)) where a <c<b, then fƒ"(c)=0
7) If c is a critical number of f where a <c<band f"(c) <0 on (a,b), then f has a relative
minimum at x = c
8)
The graph of a function f(x) cannot intersect its vertical asymptote.
9) The graph of a function f(x) cannot intersect its horizontal asymptote.
10) If f(x) is not continuous on the interval [a,b] then f(x) cannot have an absolute maximum
value.
11) If f(x) is defined on a closed interval [a,b] then f(x) has an absolute minimum value.
12) If f(x) is continuous on [a,b], f(x) is differentiable on (a,b), and f'(x) #0 for all x in (a,b),
then the absolute maximum value of f(x) on [a,b] is f(a) or f(b).
13) If x <y, then e* <e"
14) If 0<b<1 and x<y, then b* >b²
15) If e** >0 then k>0 and x>0.
16) f(x) = ex is an increasing function if k>0 and a decreasing function if k<0.
17) (In x³)=3 lnx for all x in (0,00)
18) If a>0 and b>0 then In(a+b) = ln a + ln b
19) If b>0, then enb= ln e
20) If f(x)=3" then f'(x) = x3-¹
21) If f(x) = e²
then f'(x) = e
22) If ƒ(x) = π*
then f'(x) = n*
23) If f(x)=e³x² then f'(x) = ex
1
24) f(x) = ln |x| then f'(x):
25) f(x) = ln 5 then f'(x) =
P
26) f(x) = ln(x+5)² then f'(x) =
x
1
(x + 5)²
27) If you are modeling exponential decay, you can use a model of the form Q(t)=Qe
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