Math 125       Test 3           8 points each          March 15, 2006

 


Differentiate

 

1.

 

2.

 

3.  y = sec 4x cos x2

 

4.    y = ¹ tan20 4x

 

5.

 

6. Find the equation of the line tangent to

 

f(x) = sin (¹x) at x = 1/3

 

Find all max and min and sketch the function.

7.   on the interval [-1,2]

 

Sketch Graph without calculus:

 

8. y = (x  - 2)2 (x + 3)3 (x - 1)2

 

9. 

Find max's, min's, inflection points and sketch accurate graph of the functions, tell whether each max or min is relative or absolute.

 

10. y =  x3 - 3x2 + 3

 

 

 Write the equation for:

11.

 

 

 

12.  The height of a right triangle remains fixed at 6 m while the base expands at a constant rate of  3 m/s.  Find the rate of change of the area of the triangle at the instant the base is 8 m.

 

10 points Bonus!

Find max's, min's, inflection points and sketch accurate graph of the functions, tell whether each max or min is relative or absolute.