requestbook

Step-by-step Answer
PAGE: 403SET: ExercisesPROBLEM: 9
Please look in your text book for this problem Statement

(a)

The function .

Find the -intercept:

Find the -intercept, by substituting in .

.

The -intercept is .

(b)

The function and the interval is .

Differentiate the function with respect to :

Determination of critical points:

The critical points exist when .

Equate to zero:

Solve in the interval .

General solution of is , where is an integer.

General solution is

If , .

If , .

The solutions are in the interval .

The critical points are and the test intervals are .

Interval Test Value Sign of Conclusion

Decreasing

Increasing

Decreasing

The function is increasing over the interval .

(c)

The function and the interval is .

The critical points are .

Find the values of at these critical points.

.

.

Find the values of at the end points of the interval.

.

.

Compare the four values of to find the absolute maximum.

Absolute maximum value is .

(d)

The function and the interval is .

General solution of is , where image is an integer.

General solution: .

If image, .

If image, .

If image, .

The solutions are and in the interval .

(e)

The function and the interval is .

General solution of image is image, where image is an integer.

General solution: .

If image, .

If image, .

If , .

If image, .

The solution is and in the interval .

General solution of image is image, where image is an integer.

General solution: .

If image, .

If image, .

If image, .

If , .

The solution is and in the interval .

(f)

General solution of image is image, where image is an integer.

General solution: .

If image, .

If image, .

If , .

If image, .

If , .

If , .

The solutions are and in the interval .

(g)

Find the -intercept:

The function .

Find the -intercept, by substituting in .

General solution of is , where image is an integer.

The -intercepts are , where image is an integer.

(a). The -intercept is .

(b).The function is increasing over the interval .

(c). Absolute maximum value is .

(d).The solutions are and in the interval .

(e). For , the solutions are and in the interval .

For , the solutions are and in the interval .

(f). The solutions are and in the interval .

(g).The - intercepts are , where image is an integer.



TESTIMONIALS

"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!"

June Barnett

"Your site is amazing! It helped me get through Algebra."

Charles

"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful."

Dan Pease

QUESTIONS? LET US HELP.
Simply chose a support option

My status

JOIN US ON:     
mathskey.com is not affiliated with any Publisher, Book cover, Title, Author names appear for reference only