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# Intervals of Increase and Decrease (Grades 11-12)

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## Intervals of Increase and Decrease

1.
What are all the values of $x$ for which the function $f$ defined by $f(x)=x^3+3x^2-9x+7$ is increasing?
1. $-3< x<1$
2. $-1< x< 1$
3. $x<-3$ and $x>1$
4. $x<-1$ and $x>3$
5. All real numbers
2.
On what intervals is the function $f(x)=3x^3+2x^2$ increasing or decreasing?
1. Increasing: $(-oo,-4/9) uu (0, oo)$, decreasing: $(-4/9, 0)$
2. Increasing: $(-oo,-4/9)$, decreasing: $(-4/9, 0)$
3. Increasing: $(-oo,0) uu (-4/9, oo)$, decreasing: $(-4/9, 0)$
4. Increasing: $(-4/9, 0)$, decreasing: $(-oo,-4/9) uu (0, oo)$
3.
Identify the intervals on which the given function is increasing and decreasing.
$f(x)=x^3+x^2-x$
1. Increasing: $(-oo, -1) uu (1/3,oo)$; decreasing: $(-1, 1/3)$
2. Increasing: $(-oo, -1)$; decreasing: $(-1, 1/3)$
3. Increasing for all x
4. Increasing: $(-1,1/3)$; decreasing: $(-oo, -1) uu (1/3,oo)$
4.
$f(x)=2x^5+x^3-3x$ is
1. increasing on $(-oo,oo)$.
2. decreasing on $(-oo,-0.65)cup(0.65,oo)$ and increasing on $(-0.65,0.65)$.
3. increasing on $(-oo,-0.65)cup(0.65,oo)$ and decreasing on $(-0.65,0.65)$.
4. decreasing on $(-oo,-1.4)cup(1.4,oo)$ and decreasing on $(1.4,-1.4)$.
5.
Find the intervals of increase and decrease. $f(x) = e^x (3x^2 + 2x - 5)$
1. Increase: $(-oo,-3) uu (0,1/3); \ \$ Decrease: $(-3,0) uu (1/3,oo)$
2. Increase: $(-oo,-3) uu (1/3,oo); \ \$ Decrease: $(-3,1/3)$
3. Increase: $(-3,0) uu (1/3,oo); \ \$ Decrease: $(-oo,-3) uu (0,1/3)$
4. Increase: $(-3,1/3); \ \$ Decrease: $(-oo,-3) uu (1/3,oo)$
6.
If $f(x)=(lnx)/x$, for all $x>0$, which of the following is true?
1. f is increasing for all x greater than 0
2. f is increasing for all x greater than 1
3. f is decreasing for all x between 0 and 1
4. f is decreasing for all x between 1 and e
5. f is decreasing for all x greater than e
7.
Find where the function $f(x) = xln(x^2)$ is increasing and where it is decreasing.
1. Increasing on $(-oo,0)$ and decreasing on $(0,oo)$
2. Increasing on $(-oo,-1/e) uu (1/e, oo)$ and decreasing on $(-1/e,0) uu (0,1/e)$
3. Increasing on $(-1/e,0) uu (0,1/e)$ and decreasing on $(-oo,-1/e) uu (1/e, oo)$
4. Increasing on $(-oo,oo)$
8.
Determine the intervals of increase and decrease. $f(x) = x^2/(x^2-1)$
1. Increasing on $(-oo,0)$ and decreasing on $(0,oo)$
2. Increasing on $(-sqrt(2),0) uu (sqrt(2),oo)$ and decreasing on $(-oo,-sqrt(2)) uu (0,sqrt(2))$
3. Increasing on $(-oo,-1) uu (1,oo)$ and decreasing on $(-1,1)$
4. Increasing on $(-oo,-1) uu (-1,0)$ and decreasing on $(0,1) uu (1,oo)$
9.
Identify the intervals on which the given function is increasing and decreasing.
$f(x)=x^2 e^(-x^2)$
1. Increasing: $(-oo, -1) uu (0,1)$; decreasing: $(-1, 0) uu (1,oo)$
2. Increasing: $(-oo, 0)$; decreasing: $(0, oo)$
3. Increasing for all x
4. Increasing: $(-1,0) uu (1,oo)$; decreasing: $(-oo, -1) uu (0,1)$
10.
Find the intervals of increase and decrease for the following function. $f(x) = sqrt(3x^2 - 9x + 6)$
1. Increasing on $(3/2,oo)$ and decreasing on $(-oo, 3/2)$
2. Increasing on $(2,oo)$ and decreasing on $(-oo,1)$
3. Increasing on $(3/2,oo)$
4. Increasing on $(2,oo)$
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