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Maze
Freestyle
High 12
Math
FTC(2)
Hyesung Kang
26
1
Added question (10/ 20)
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# 1

Multiple Choice

If g(x) = ∫[a to x] f(t) dt, what is g'(x)?

  • f(x)
  • f(a)
  • f'(x)
  • 0

# 2

Multiple Choice

If f(x) = 3x^2, what is the derivative of g(x) = ∫[0 to x] f(t) dt?

  • 3x^2
  • 6x
  • x^3
  • 9x^2

# 3

Multiple Choice

If f(x) is a constant function, what is the derivative of g(x) = ∫[a to x] f(t) dt?

  • f(x)
  • 0
  • c
  • f'(x)

# 4

Multiple Choice

If a function is continuous on the interval [a, b], what does the Mean Value Theorem for Integrals guarantee?

  • The function has a maximum at x = a.
  • There exists a number c in [a, b] such that the integral is zero.
  • There exists a number c in [a, b] such that the area under the curve equals the area of a rectangle with height f(c).
  • The function is differentiable on (a, b).
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