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Twelfth Grade (Grade 12) Derivatives Questions

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Grade 12 Derivatives
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]
Grade 12 Derivatives
What is the second derivative of [math]f(x)=3x^3+2x^2[/math]?
  1. [math]f''(x)=18x+4[/math]
  2. [math]f''(x)=9x^2+4x[/math]
  3. [math]f''(x)=18[/math]
  4. [math]f''(x)=0[/math]
Grade 12 Derivatives
Differentiate. [math]f(x) = (4x^100)/25[/math]
  1. [math] f'(x) = (4x^99)/25[/math]
  2. [math] f'(x) = (8x^10) / 5 [/math]
  3. [math] f'(x) = x^99 / 625 [/math]
  4. [math] f'(x) = 16x^99[/math]
Grade 12 Derivatives
Find the derivative. [math] f(x) = root[5](x^7) [/math]
  1. [math] f'(x) = root[5](7x^6) [/math]
  2. [math] f'(x) = 7/5 root[5](x^2) [/math]
  3. [math] f'(x) = root[4](x^6) [/math]
  4. [math] f'(x) = root[5](x^2) [/math]
Grade 12 Derivatives
Differentiate. [math] f(x) = 3x^4 + 9sqrt(x) - 7/root[3](x^4) [/math]
  1. [math] f'(x) = 12x^3 + 9sqrt(x) + 7/(4root[3](x^3)) [/math]
  2. [math] f'(x) = 12x^3 + 9/2 sqrt(x) +21/(4root[3](x)) [/math]
  3. [math] f'(x) = 12x^3 + 9/(2sqrt(x)) + 28/(3root[3](x^7)) [/math]
  4. [math] f'(x) = 12x^3 +9 - 7/root[3](4x^3) [/math]
Grade 12 Derivatives CCSS: HSF-IF.C.7c
On [math]f(x)=2x^5+x^3-3x[/math]
  1. [math](-0.65,1.4)[/math] is a relative and absolute maximum.
  2. [math](0.65,-1.4)[/math] is a relative and absolute minimum.
  3. [math](-0.65,1.4)[/math] is a relative maximum.
  4. [math](0.65,-1.4)[/math] is a relative minimum.
  5. Both A and B.
  6. Both C and D.
  7. None of the above.
Grade 12 Derivatives
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
Grade 12 Derivatives
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]
Grade 12 Derivatives
What is the derivative of [math]f(x)=3x^3+2x^2[/math]?
  1. [math]f'(x)=9x^2+4x[/math]
  2. [math]f'(x)=3x^2+2x[/math]
  3. [math]f'(x)=0[/math]
  4. [math]f'(x)=12x^2+6x[/math]
Grade 12 Derivatives
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]
Grade 12 Derivatives
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]
Grade 12 Derivatives CCSS: HSF-IF.C.7c
[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]
Grade 12 Derivatives
What are the critical numbers of the following equation?
[math]f(x)=3x^3+2x^2[/math]
  1. [math]x=-4/9, 0[/math]
  2. [math]x=4/9, 0[/math]
  3. [math]x=-9/4, 0[/math]
  4. [math]x=9/4, 0[/math]
Grade 12 Derivatives
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]
Grade 12 Derivatives
On what intervals is the function [math]f(x)=3x^3+2x^2[/math] concave upwards and downwards?
  1. concave upward [math](-2/9, oo)[/math], concave downward [math](-oo, -2/9)[/math]
  2. concave upward [math](-oo, -2/9)[/math], concave downward [math](-2/9, -oo)[/math]
  3. concave upward [math](0, oo)[/math], concave downward [math](-oo, 0)[/math]
  4. concave upward [math](-oo, 0)[/math], concave downward [math](0, oo)[/math]
Grade 12 Derivatives
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]
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