6. For each function determine:

i) the critical values

ii) the intervals of increasing or decreasing

iii) the maximum and minimum points.

1. f (x)=4x^2 +12x7
2. f (x)= x^3 9x^2 +24x 10
3. y =x^2/ x^2 +2x 15

7. Find the intervals of concavity for the function and state the points of inflection.

a. f (x)= x^4 2x^3 + x 2

b. f (x)= x^2/x^2 4

8. Using the second derivative test, find the maximum and minimum points for the function

f (x)= x^4 8x^2 +5

9. What conclusion can be made if:

a. A function changes from a decreasing interval to an increasing interval.

b. lim f (x)= and lim f (x)=

x 0+ x 0

10. If the maximum of the function y = x^2 4x+21 occurs at x =2, what are the

coordinates of the maximum point? (1 mark)

Use the curve sketching procedure to analyze the function.

a. y = x^3 + x^2 20x

b. y = 1+x^2 /1x^2