Chapter 1.

1.1 Problem Statement

rand(2,9)
round($m*sqrt(2),2)

Find the critical points of f(x) = $m·sin(x) +$m·cos(x) and determine the extreme values on .

1.2 Step 1

Question Sequence

Question 1.1

A number c in the domain of f is called a critical point if f'(c) =1Wh3cvJ2xF4= or where f'(c)risoekzpYAAgRXECVAcsXWXnXFT9zJ4gDoyL7g==.

Correct.
Incorrect.

Question 1.2

The extreme values (absolute maximum and absolute minimum) of a continuous function on a closed interval occur either at a veUJQTOZK4x9ROLR9ZowuS+REowc07GT0ub4zJSXu3Q9LVxQoTWeVA== of the function or at the PYUF4jajY92ZPh6isbc26od3QKQqgM0X of the closed interval.

Correct.
Incorrect.

1.3 Step 2

Thus, we need to find the critical points of f(x) = $m·sin(x) +$m·cos(x) in and then compare the function values at these critical points with the function values at the endpoints of to find the extreme values.

Question Sequence

Question 1.3

Find f'(x).

f(x) = $m·sin(x) +$m·cos(x)

f'(x) = RzFwHiTkGvzaVYltE1Vrml6jTAx0cim8bOmIi2p0RXVaf12GO3D9Ih2tPHYdOtDWW3dGrTznjaldZLxXQoKvBSFmMQE4vyH7hWWm2CyMBxfbugZAto/kz8WRxLXy8cHanqjylW8gWuXiOrHP8ANuLA==

Correct.
Incorrect.

Question 1.4

f'(x) is TMCjkDkjHOoWmmLY0MxjDvhFWoaLycK4Eqqij+SwweBTVXh9y0tudN3mhxfzq1uc2Qyn5TQPNyl4tHP4GOxQTw==.

Correct.
Incorrect.

1.4 Step 3

Solve f'(x) = 0 for to find any critical points, c.

Question Sequence

Question 1.5

f'(x) = 0

$m·sin(x) + $m·cos(x) = 0

sin(x) = cos(x)

tan(x) = 0VV1JcqyBrI=

Correct.
Incorrect.

Question 1.6

Thus, the critical point on that satisifes this equation is

c = KP7xRuJeu2MMVdBrp+D41A==.

Correct.
Incorrect.

1.5 Step 4

Compare the values of f(x) = $m·sin(x) + $m·cos(x) at the critical point x = and the endpoints of . The greatest value is the absolute maximum and the smallest value is the absolute minimum of f(x) on .

Question Sequence

Question 1.7

nzZK80z5Ma1gnSaj.

xf1an8qan6o=.

xf1an8qan6o=.

(Round your answers to two decimal places.)

Correct.
Incorrect.

1.6 Step 5

Question Sequence

Question 1.8

The minimum value of f is xf1an8qan6o=.

The maximum value of f is nzZK80z5Ma1gnSaj.

(Round your answers to two decimal places.)

Correct.
Incorrect.