help? plz? (critical points -extrema]

Question

Answer 1

(11)

Step 1:

The function is and interval is .

Absolute maxima or minima are exist either at the end points or at the critical numbers.

Find the critical numbers :

is differentiable at all points because its a polynomial.

Therefore the solutions of are the only critical numbers.

Differentiate on each side with respect to t.

Equate to zero.

and and

and and

The critical number are , and .

The end points are and .

Comments

Contd....

Step 2:

Find the value of f  at the critical numbers.

Substitute in .

.

Substitute in .

.

Substitute in .

.

Step 3:

Find the value of f  at the end points of the interval.

Substitute in .

.

Substitute in .

.

Since the largest value is , absolute maximum is .

Since the smallest value is , absolute minimum is .

Solution :

Absolute maximum is .

Absolute minimum is .

Answer 2

(12)

Step 1:

The function is and interval is .

Absolute maxima or minima are exist either at the end points or at the critical numbers.

Find the critical numbers :

is differentiable at all points because its a polynomial.

Therefore the solutions of are the only critical numbers.

Differentiate on each side with respect to x.

Equate to zero.

The critical number are .

The end points are and .

Step 2:

Find the value of h  at the critical numbers.

Substitute in .

.

Comments

Contd.....

Find the value of h  at the end points of the interval.

Substitute in .

.

Substitute in .

.

Since the largest value is , absolute maximum is .

Since the smallest value is , absolute minimum is .

Solution :

Absolute maximum is .

Absolute minimum is .