(1)

Step 1: \ \

The function is .

Critical number :

A critical number of a function f is a number c in the domain of f such that either or does not exist. \ \

is differentiable at all values of x because it is a polynomial.

Therefore the solutions of are the critical numbers.

Differentiate on each side with respect to x.

Step 2:

.

Equate to zero.

and

and

Critical numbers are and .

Solution : \ \

Critical numbers are and .

(2)

Step 1: \ \

The function is .

Critical number :

A critical number of a function f is a number c in the domain of f such that either or does not exist. \ \

Therefore the solutions of are the critical numbers.

Differentiate on each side with respect to t.

Step 2:

.

Equate to zero.

and

and

Critical numbers are and .

Solution : \ \

Critical numbers are and .

(3)

Step 1: \ \

The function is .

Critical number :

A critical number of a function f is a number c in the domain of f such that either or does not exist. \ \

is differentiable at all values of x because it is a polynomial.

Therefore the solutions of are the critical numbers.

Differentiate on each side with respect to a.

Step 2:

.

Equate to zero.

The general solution for sine function, if  then .

Critical number is .

Solution : \ \

Critical number is .

(4)

Step 1: \ \

The function is .

Critical number :

A critical number of a function f is a number c in the domain of f such that either or does not exist. \ \

is differentiable at all values of x because it is a polynomial.

Therefore the solutions of are the critical numbers.

Differentiate on each side with respect to x.

Step 2:

.

Equate to zero.

Critical number is .

Solution : \ \

Critical number is .