1. Consider the following.

f(x) =2x + 3

x + 2

Find the critical numbers. (Hint: Check for discontinuities.) See Example 6. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.

X= ?

Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

increasing ?

decreasing ?

Sketch the graph of the function to verify your results.

2. Consider the following.

f(x) =^25-x^2

Find the critical numbers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

increasing?_________

decreasing? _________

3 A fast-food restaurant determines the cost and revenue models for its hamburgers.

C=0.9x + 7800, 0 x 50,000

R=_1__

20,000 (65,000x x²), 0 x 50,000

(a) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answers using interval notation.)

(b) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit.

4.Consider the following.

y{-x^3+2, x 0

-x^2+4x, x > 0

Find the open intervals on which the function is increasing or decreasing

Increasing?________

Decreasing?_______

5.Consider the following.

f(x) = 2x + 3

x + 2

Find the critical numbers. (Hint: Check for discontinuities.) See Example 6. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

x= _____

Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

increasing ? ______

decreasing? ______

Sketch the graph of the function to verify your results

6.Find all relative extrema of the function. (If an answer does not exist, enter DNE.)

f(x) = 3x² + 3x + 7

relative maximum(x, y)=

relative minimum(x, y)=

7.Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (Round your answers to two decimal places. If an answer does not exist, enter DNE.)

g(x) = (x² 1)^2/3,[6, 5]

absolute maximum(x, y)= absolute minimum(x, y)= (smaller x-value) (x, y)= (larger x-value)

8.Find all relative extrema of the function. (If an answer does not exist, enter DNE.)

f(x) = x⁴ 8x³

relative maximum(x, y)=

relative minimum(x, y)=

9.Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.)

h(t) = _t__ ,[5, 9]

t - 4

absolute maximum(t, y)=

absolute minimum(t, y)=