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
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