AP Calculus Review – Extrema/Graph Sketching
1. Sketch Graph of f(x) = x2/3(3 - 2x1/3)
Domain
____________________
Interval(s) of Increase _______________________
Zeroes
__________________
Interval(s) of Decrease _______________________
Relative Minima ________________
Interval(s) of Conc. Up ______________________
Relative Maxima ________________
Interval(s) of Conc. Down ____________________
Inflection Point(s)_____________________
2. Find intervals of increase and decrease for f(x) = x 2 
2
x
Interval(s) of Increase ______________________ Interval(s) of Decrease ______________________
3. Find the coordinates of the absolute min and max for f(x) = x lnx on interval (0.1,2]
Absolute Maximum _________________ Absolute Minimum _________________
What is the absolute minimum value of the function f(x) = ex x -2 on the interval [1,4]
4.
b) e2/4
a) e
5.
c) e4/16
d)1
If f(x) is the function that has the first derivative of f ′(x) =
e) none of the above
x
what is the x coordinate of
x  x 1
3
the inflection point of f(x)
a) 1.008
b) 0.473
c) 0
d)-0.278
e) there are no inflection pts
6. The relative minima of the function f(x) = cos2(x) + cos(x) on the interval (0,2π) are located at x =
a) π
b) 2 π/3, π, 4 π/3
c) 2 π/3, 4 π/3
d)0, π, 2π
e)none of the above
7. If f(x) = x3 +ax2 + bx +c and f(1) = -28, x = 4 is a relative minimum, and x=1 is an inflection point, find
the values of a and b and c.
a = ____________________
b = ___________________ c = ____________________
8. Find the coordinates all inflection points of f(x) = (x2 – 2)2/3
9. What is the smallest possible slope to the curve y = x3 – 3x2 + 5x -1?
10. Find the value(s) of x = c where the Mean Value Theorem applies to f(x) = tan 1 (3x) on the interval
[0, 1/3] . If MVT does not apply explain why not?
11. Find the value(s) of x = c where Rolle’s Theorem applies to f(x) =
[-3, 2] . If Rolle’s Theorem does not apply explain why not?
is on the interval
12. Find the value(s) of x = c where the Mean Value Theorem applies to f(x) = (2x+5)2/3
on the interval [-3,3 ] . If MVT does not apply explain why not?