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Use the second derivative test to find all relative extrema for each function.

0 votes
f(x)=x^2-6x+3

f(x)=2x^3-3x^2-12x+2015

f(x)=e^(1-2x^2)
asked Sep 9, 2015 in CALCULUS by anonymous
reshown Sep 9, 2015 by bradely

3 Answers

0 votes

(1)

The function is image.

Apply derivative with respect to .

image

Find the relative extrema by equating image to zero.

image

Consider image.

Apply derivative with respect to .

image

image.

image is positive for all values of .

Therefore, the function has relative minimum at image.

image.

Relative minima is image.

No relative maxima.

answered Sep 9, 2015 by cameron Mentor
edited Sep 9, 2015 by cameron
0 votes

(2)

Step 1:

The function is .

Apply derivative with respect to .

Find the relative extrema by equating to zero.

and .

Substitute  in .

The point is image.

Substitute  in .

image

The point is image.

The relative extrema points are image and image.

Step 2:

Using second derivative test, determine the relative extrema.

Consider .

Apply derivative on each side with respect to .

.

Relative minima is image.

Relative maxima is image.

Solution:

Relative minima is image.

Relative maxima is image.

answered Sep 9, 2015 by cameron Mentor
edited Sep 9, 2015 by bradely
0 votes

(3)

Step 1:

The function is image.

Apply derivative with respect to .

image

Find the relative extrema by equating to zero.

image

Substitute image in image.

image

The extrema point is image.

Step 2:

Using second derivative test, determine the relative extrema.

Consider image.

Apply derivative with respect to .

image

Find the sign of image at image.

image

Therefore, the function has relative maximum at image.

The relative maximum is image.

No relative minima.

Solution:

The relative maximum is image.

No relative minima.

answered Sep 9, 2015 by cameron Mentor
edited Sep 9, 2015 by cameron

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