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help-critical points-extrema

0 votes

asked May 3, 2015 in CALCULUS by anonymous

4 Answers

0 votes

(1)

Step 1:

The function is image.

Critical number :

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

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

Therefore the solutions of image are the critical numbers.

Differentiate on each side with respect to x.

image

Step 2:

image.

Equate to zero.

image

image and image

image and image

Critical numbers are image and image.

Solution :

Critical numbers are image and image.

answered May 4, 2015 by joseph Apprentice
0 votes

(2)

Step 1:

The function is image.

Critical number :

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

Therefore the solutions of image are the critical numbers.

Differentiate image on each side with respect to t.

image

Step 2:

image.

Equate image to zero.

image

image and image

image and image

Critical numbers are image and image.

Solution :

Critical numbers are image and image.

answered May 4, 2015 by joseph Apprentice
0 votes

(3)

Step 1:

The function is image.

Critical number :

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

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

Therefore the solutions of image are the critical numbers.

Differentiate image on each side with respect to a.

image

Step 2:

image.

Equate image to zero.

image

The general solution for sine function, if image then image.

image

Critical number is image.

Solution :

Critical number is image.

answered May 4, 2015 by joseph Apprentice
0 votes

(4)

Step 1:

The function is image.

Critical number :

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

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

Therefore the solutions of image are the critical numbers.

Differentiate on each side with respect to x.

image

Step 2:

image.

Equate to zero.

image

Critical number is image.

Solution :

Critical number is image.

answered May 4, 2015 by joseph Apprentice

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