1. Consider the following graph of a function.

a) Find and if they exist.

b) Where is the function continuous? (Excluding endpoints)

c) Where is the function differentiable? (Excluding endpoints)

2. Find the following limits

a) b) c)

3. You inflate a spherical balloon at a constant rate such that its radius is changing at a rate of 2cm/s when the radius is 3cm. How hard are you blowing? (Hint the volume of a sphere: )

4. Find the tangent line to at the point (2,1).

5. Draw a picture of the graph of . For your convenience the first two derivatives of this are and .

6. Use the definition of the derivative to find the derivative of . Use this information to find the tangent line to this function at the point (-1,1).

7. Find the following derivatives in terms of

a) b)

8. Show that among all rectangles of a fixed perimeter P (constant) that a square has the largest area.

9. Let f(x) be a function that satisfies the following conditions

a) f(0)=f(4)=0, f(x)>0 if x<0 and f(x)<0 if x>0 and x is not 4

b)f’(-2)=f’(2)=0

c)f’(x)>0 on the intervals x<-2 and (2,4)

d)f’(x)<0 on the interval (-2,2)

e)f’(x)=-1 on the interval x>4

f)f’’(x)>0 on the intervals x<-3 and (0,4)

g)f’’(x)<0 on the interval (-3,0)

h)f’’(x)=0 on the interval x>4

Sketch the graph of f(x).

10. Let be a constant. Find the area under the curve , .