Find the absolute maximum and absolute minimum values of f on the given interval.

Question

f(t) = 2cos t + sin 2t,    [0, π/2]

absolute min value=?

absolute max value=?

Answer 1

Step 1:

The function is on interval .

Apply derivative on each side with respect to .

.

Step 2:

Find the critical numbers of on the interval .

Solve .

and

and

and .

Sine function is negative in the third quadrant and fourth quadrant which is not in

the interval .

The solutions of are not in the interval .

Comments

Contd...

Solve .

The general solution of , then , where is an integer.

Take .

.

Take .

.

Consider solutions in the interval .

is not in the interval.

The solution of is .

Step 3:

Substitute in .

.

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

.

.

The function has absolute maximum is .

The function has absolute minimum is .

Solution:

The function has absolute maximum is .

The function has absolute minimum is .