AP CALCULUS BC PROBLEM SET 4
1.
1969 - AB 1
Consider the following functions defined for all x:
f1(x) = x
f2 (x) = xcos x
f3(x) = 3e2x
f4 (x) = x - x
Answer the following questions (a, b, c,and d) about each of these functions. Indicate your answer by
writing either yes or no in the appropriate space in the given rectangular grid. No justification is required,
but each blank space will be scored as an incorrect answer.
FUNCTIONS
QUESTIONS
f
f
f
f
(a) Does fxfx?
(b) Does the inverse function exist for all
x?
(c) Is the function periodic?
(d) Is the function continuous at x  ?
2.
3.
1998 AB 6
Consider the curve defined by 2y 3 + 6x 2 y -12x 2 + 6y = 1 .
dy
4x - 2xy
(a) Show that
.
= 2
dx x + y2 +1
(b) Write an equation of each horizontal tangent line to the curve.
(c) The line through the origin with slope -1 is tangent to the curve at point P . Find the x- and ycoordinates of the point P .
1978 - AB 2
Let f ( x)  1  x  for all real numbers x, and let gxln x for all xLet h( x)  1  ln x  .
2
4.

5.

(a) Determine whether hxis the composition fgx or gfx .

(c) Find hx 

(d)
Sketch the graph of h.
1979 - AB 6
The curve f ( x)  x 2  2 x is defined for for all real numbers x.
(a) Sketch the graph of yfx
(b) Determine whether the derivative of fxexists at
x Justify your answer.
(c) Sketch the graph of  y fx
(d) Determine whether fx is continuous at xJustify your
answer.
2
(b)
Find hx








1981 - AB 1
Let f be the function defined by f ( x)  x4  3x2  2 .
(a) Find the zeros of f.
(b) Write an equation of the tangent line to the graph of f at the point where x
(c) Find the x-coordinate of each point at which the line tangent to the graph of f is parallel to the line
yx