A(1)

The function is .

Differentiate with respect to x.

To find the critical points, equate to zero.

Critical number is .

Substitute in the function.

Therefore the critical point is .

A-(2)&(3)

The function is .

From A-(1), the critical point is .

The derivative function is .

Consider test intervals as and .

\ Interval \	Test Value	Sign of	Conclusion
		\ \	Decreasing
		\ \	Increasing

Therefore the function is increasing in the interval .

The function is decreasing in the interval .

Solution:

A-(2): The function is increasing in the interval .

A-(3): The function is decreasing in the interval .

A-(4)&(5)

The function is .

From A-(1), the critical number is .

The derivative function is .

Differentiate with respect to x.

The sign of is positive for all values of x.

Therefore, the function has relative minimum at .

Relative minima is .

No relative maxima.

Solution:

A-(4): Relative minima is .

A-(5): No relative maxima.

B(1)

The function is .

Differentiate with respect to .

.

To find the critical points, equate to zero.

Critical number is .

Substitute in the function.

Therefore the critical point is .

B-(2)&(3)

The function is .

From A-(1), the critical point is .

The derivative function is .

Consider test intervals as and .

\ Interval \	Test Value	Sign of	Conclusion
		\ \	Increasing
		\ \	Decreasing

Therefore the function is increasing in the interval .

The function is decreasing in the interval .

Solution:

B-(2): The function is increasing in the interval .

B-(3): The function is decreasing in the interval .

B-(4)&(5)

The function is .

From B-(1), the critical number is .

The derivative function is .

Differentiate with respect to x.

.

Find the value of second derivative at .

.

Therefore, the function has relative maximum at .

Relative maxima is .

No relative maxima.

Solution:

B-(4): Relative minima is .

B-(5): No relative minima.