AP Calculus BC Unit 5 Progress Check:
MCQ Part A Exam
Let f be the function given by f(x)=cos(x^2+x)+2 The derivative of f is given by f'(x)=-
(2x+1)sin(x^2+x). What value of c satisfies the conclusion of the Mean Value Theorem
applied to f on the interval [1,2]? - Correct Answers -B. 1.438 because f'(x)= f(2)-f(1)/(2-
1)
The derivative of the function f is given by f'(x)= sqrt(x) sin(3sqrt(3sqrt(x)) On which of
the following intervals in [0,6pi] is f decreasing? - Correct Answers -C. [1.097,4.386],
[9.870,17.546]
The concentration of a certain element in the water supply of a town is modeled by the
function f, where f(t) is measured in parts per billion and t is measured in years. The first
derivative of f is given by f'(t)=1-lnt-sint. At what times t, for 0<t<5 does the
concentration attain a local minimum? - Correct Answers -C. t=3.353 only
Selected values of a continuous function f are given in the table above. Which of the
following statements could be false? - Correct Answers -By the Mean Value Theorem
applied to f on the interval [0,4], there is a value c such that f'(c)=4
Let f be the function defined by f(x)=3x^3−36x+6 for −4<x<4. Which of the following
statements is true? - Correct Answers -f is decreasing on the interval (-2,2) because
f'(x)<0 on the interval (-2,2).
Let f be the function defined by f(x)=x33−x22−6x. On which open intervals is f
decreasing? - Correct Answers -A. -2<x<3 only
Let f be a function with first derivative given by f′(x)=(x+1)(x−2)(x−3). At what values of x
does f have a relative maximum? - Correct Answers -A. 2 Only
The graph of f′, the derivative of the function f, is shown above for −1<x<5. Which of the
following statements is true for −1<x<5 ? - Correct Answers -f has two relative minima
and one relative maximum.
Let f be the function given by f(x)=(x^2-9)/sinx on the closed interval [0,5]. Of the
following intervals, on which can the Mean Value Theorem be applied to f? - Correct
Answers -C. I and II only
MCQ Part A Exam
Let f be the function given by f(x)=cos(x^2+x)+2 The derivative of f is given by f'(x)=-
(2x+1)sin(x^2+x). What value of c satisfies the conclusion of the Mean Value Theorem
applied to f on the interval [1,2]? - Correct Answers -B. 1.438 because f'(x)= f(2)-f(1)/(2-
1)
The derivative of the function f is given by f'(x)= sqrt(x) sin(3sqrt(3sqrt(x)) On which of
the following intervals in [0,6pi] is f decreasing? - Correct Answers -C. [1.097,4.386],
[9.870,17.546]
The concentration of a certain element in the water supply of a town is modeled by the
function f, where f(t) is measured in parts per billion and t is measured in years. The first
derivative of f is given by f'(t)=1-lnt-sint. At what times t, for 0<t<5 does the
concentration attain a local minimum? - Correct Answers -C. t=3.353 only
Selected values of a continuous function f are given in the table above. Which of the
following statements could be false? - Correct Answers -By the Mean Value Theorem
applied to f on the interval [0,4], there is a value c such that f'(c)=4
Let f be the function defined by f(x)=3x^3−36x+6 for −4<x<4. Which of the following
statements is true? - Correct Answers -f is decreasing on the interval (-2,2) because
f'(x)<0 on the interval (-2,2).
Let f be the function defined by f(x)=x33−x22−6x. On which open intervals is f
decreasing? - Correct Answers -A. -2<x<3 only
Let f be a function with first derivative given by f′(x)=(x+1)(x−2)(x−3). At what values of x
does f have a relative maximum? - Correct Answers -A. 2 Only
The graph of f′, the derivative of the function f, is shown above for −1<x<5. Which of the
following statements is true for −1<x<5 ? - Correct Answers -f has two relative minima
and one relative maximum.
Let f be the function given by f(x)=(x^2-9)/sinx on the closed interval [0,5]. Of the
following intervals, on which can the Mean Value Theorem be applied to f? - Correct
Answers -C. I and II only
