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Twelfth Grade (Grade 12) Calculus Questions

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Grade 12 Derivatives
On what intervals is the function f(x)=3x3+2x2 increasing or decreasing?
  1. Increasing: (-∞,-49)∪(0,∞), decreasing: (-49,0)
  2. Increasing: (-∞,-49), decreasing: (-49,0)
  3. Increasing: (-∞,0)∪(-49,∞), decreasing: (-49,0)
  4. Increasing: (-49,0), decreasing: (-∞,-49)∪(0,∞)
Grade 12 Limits
Evaluate the limit. limx→0(x-5)2-25x
  1. Does not Exist
  2. -10
  3. ∞
  4. 0
Grade 12 Derivatives
Find the intervals of increase and decrease for the following function. f(x)=√3x2-9x+6
  1. Increasing on (32,∞) and decreasing on (-∞,32)
  2. Increasing on (2,∞) and decreasing on (-∞,1)
  3. Increasing on (32,∞)
  4. Increasing on (2,∞)
Grade 12 Derivatives
What are all the values of x for which the function f defined by f(x)=x3+3x2-9x+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
Grade 12 Derivatives
Identify the intervals on which the given function is increasing and decreasing.
f(x)=x2e-x2
  1. Increasing: (-∞,-1)∪(0,1); decreasing: (-1,0)∪(1,∞)
  2. Increasing: (-∞,0); decreasing: (0,∞)
  3. Increasing for all x
  4. Increasing: (-1,0)∪(1,∞); decreasing: (-∞,-1)∪(0,1)
Grade 12 Derivatives
Find ddx(tan-1(x-√a2-x2x+√a2-x2)).
  1. -1√a2-x2
  2. 1√a2-x2
  3. √a2-x2
  4. x√a2-x2
Grade 12 Limits
Is h(x)=x-4x2-5x+4 continuous or discontinuous at x = 1? Justify using continuity test. If discontinuous, what type?
  1. Continuous
  2. Infinite discontinuity
  3. Jump discontinuity
  4. Removable discontinuity
Grade 12 Derivatives
What are the critical numbers of the following equation?
f(x)=3x3+2x2
  1. x=-49,0
  2. x=49,0
  3. x=-94,0
  4. x=94,0
Grade 12 Integrals
What is the indefinite integral of f(x)=3x3+2x2?
  1. ∫3x3+2x2dx=3x44+2x33+C
  2. ∫3x3+2x2dx=9x2+4x+C
  3. ∫3x3+2x2dx=3x3+2x2+C
  4. ∫3x3+2x2dx=4x33+3x22+C
Grade 12 Limits
What is limx→∞1ex?
  1. -∞
  2. 0
  3. e
  4. ∞
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