Pre-Calculus, 9th edition

 PAGE: 403 SET: Exercises PROBLEM: 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 is an integer.

General solution: .

If , .

If , .

If , .

The solutions are and in the interval .

(e)

The function and the interval is .

General solution of is , where is an integer.

General solution: .

If , .

If , .

If , .

If , .

The solution is and in the interval .

General solution of is , where is an integer.

General solution: .

If , .

If , .

If , .

If , .

The solution is and in the interval .

(f)

General solution of is , where is an integer.

General solution: .

If , .

If , .

If , .

If , .

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 is an integer.

The -intercepts are , where 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 is an integer.

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