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Grade 12 College

Twelfth Grade (Grade 12) Calculus Questions

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Grade 12 Calculus
Find the average rate of change of [math]f(x)=-4x^2+3x-4[/math] on the interval [math][-1, 3][/math].
  1. [math]-1/5[/math]
  2. [math]5[/math]
  3. [math]1/5[/math]
  4. [math]-5[/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 Limits
Evaluate the limit. [math]lim_{x->5} (x^2 - 2x - 15)/(x^2 - 25) [/math]
  1. [math]0[/math]
  2. [math]4/5[/math]
  3. [math]1[/math]
  4. [math]1/2[/math]
Grade 12 Limits
Grade 12 Limits
Describe the end behavior of [math]f(x)=2^x-3[/math].
  1. [math]"As " x -> -oo, y-> -3; \ "as " x->oo, y->oo[/math]
  2. [math]"As " x -> -oo, y-> oo; \ "as " x->oo, y->oo[/math]
  3. [math]"As " x -> -3 , y-> oo; \ "as " x->oo, y->oo[/math]
  4. [math]"As " x -> -oo, y-> oo; \ "as " x->oo, y->-3[/math]
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
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 Limits
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
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 Limits
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