Download 3.1 - 3.2 Worksheet

AP Calculus
3.1 – 3.2 Worksheet
Name:
For #1 – 2, Explain why each of the following functions fails to satisfy the conditions of the Mean Value Theorem. (Hint:
you may need to make a graph as part of your explanation.)
1. f(x) =
x 1
2
 x 3  3, x  1
2. f ( x)   2
 x  1, x  1
3. Let f(x) = 1  x 2 , A = (-1, f(-1)), and B = (1, f(1)). Find a tangent to f in the interval (-1, 1) that is parallel to the line
AB.
In #4 – 6, (a) state whether or not the function satisfies the hypotheses of the Mean Value Theorem on the given
interval and (b) if it does, find each value of c on the interval (a, b) that satisfies the equation f ' (c) 
4. f(x) = x2 + 2x – 1 on [0, 1]
6. f(x) = x2/3 on [0, 1]
5. f(x) = x1/3 on [-1, 1]
f (b)  f (a )
ba
AP Calculus
Name:
3.1 – 3.2 Worksheet
For #7 – 8, find any critical numbers of the function.
8. g ( x) 
7. h(x) = sin2x + cos x, 0 < x < 2π
4x
x 1
2
For #9-12, locate the absolute extrema of the function on the closed interval.
2x
, [-2, 2]
x 1
9. g(x) = x2 – 2x, [0, 4]
10. f ( x) 
11. y = 3 - |t – 3|, [-1, 5]
12. g(x) = sec x, 
2
  
,
 6 3 
In #13 – 14, graph a function on the interval [-2, 5] having the given characteristics.
13. Absolute maximum at x = -2, absolute
14. Relative minimum at x = -1, critical number (but not an
minimum at x = 1, relative maximum at x = 3.
absolute extrema) at x = 0, absolute maximum at x = 2, absolute
minimum at x = 5
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x