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Twelfth Grade (Grade 12) Calculus Questions

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Grade 12 Calculus
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 Calculus
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 Sequences and Series
The sum to infinity of the geometric sequence [math]16, 8, 4, 2, ...[/math] is
  1. [math]8[/math]
  2. [math]16[/math]
  3. [math]32[/math]
  4. [math]64[/math]
Grade 12 Calculus
What is the area under the curve for the function [math]f(x)=3x^3+2x^2[/math] on the closed interval [math][-5,5][/math]?
  1. [math]int_-5^5(3x^3+2x^2)dx=500/3[/math]
  2. [math]int_-5^5(3x^3+2x^2)dx=3/500[/math]
  3. [math]int_-5^5(3x^3+2x^2)dx=3[/math]
  4. [math]int_-5^5(3x^3+2x^2)dx=500[/math]
Grade 12 Calculus
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 Calculus
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 Calculus
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 Calculus
Grade 12 Calculus
An equation of the line tangent to the graph of [math]y=cos(2x)[/math] at [math]x=pi/4[/math] is
  1. [math]y-1=-(x-pi/4)[/math]
  2. [math]y-1=-2(x-pi/4)[/math]
  3. [math]y=2(x-pi/4)[/math]
  4. [math]y=-(x-pi/4)[/math]
  5. [math]y=-2(x-pi/4)[/math]
Grade 12 Calculus
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
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