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1) Suppose that f(x)=x 4 +12x 3 a) Increasing: 2) Suppose that f(x)=3x?2/(x+4) a

ID: 2838792 • Letter: 1

Question

1) Suppose that f(x)=x4+12x3

a) Increasing:

2) Suppose that f(x)=3x?2/(x+4)

a) Increasing:  
b) Decreasing:  
c) Local maxima at x =  
d) Local minima at x =  
e) Concave up:  
f) Concave down:

3) Suppose that f(x)=x?3/(x2)

a) Critical value(s) =  
b) Increasing:  
c) Decreasing:  
d) Local maxima at x =  
e) Local minima at x =  
f) Concave up:  
g) Concave down:  

4) Consider the function f(x)=(x?6)x1/3

a.) The critical number(s):
b.) f(x) is increasing on the interval(s):   and decreasing on:

c.) f(x) has a local maximum at x =  and a local minimum at x =
d.) f(x) is concave up on the interval(s)  and concave down on

5) Consider the function f(x)=3cosx?cos3x for 0<x<2pi

a.) The x-intercepts are
b.) f?(x)=  .
c.) f(x) is increasing on the interval(s)
d.) f(x) is decreasing on the interval(s)   
e.) f(x) has a local maximum at x =
f.) f(x) has a local minimum at x =
g.) f??(x)=
h.) f(x) is concave up on the interval(s)
i.) f(x) is concave down on the interval(s)
j.) The x-coordinate of the points of inflection are

6) Consider the function f(x)=xlnx

a.) f(x) is increasing on the interval: and decreasing on:

b.) f(x) is concave up on the interval: and concave down on:
c.) f(x) has a point of inflection at:

Explanation / Answer

1)f(x)=x^4+12x^3

for f(x) to be increasing d/dx f(x)>0

d/dx (x^4+12x^3) =4x^3+36x^2 >0

                        4x^2(x+9)>0

                             x>-9

rest question are mot clear

Q6f(x)=xlnx

f'(x)=d/dx f(x) =1+lnx >0

                        ln x>-1

                             x>e^-1,x>.369 and decreasing from x<.369

f''(x)=1/x

for concave upward f''(x)>0,x>0-concave up and x<0 concave down,no inflexion point