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