Question

Graph the function. Then estimate any relative extrema. f(x) = -x^6 - 4x^5 + 54x^4 + 160x^3 - 641x^2 - 828x + 8,000 Graph the function. Choose the correct graph below. A. X = [- 10,10] Y = [- 10000,10000] B. X = [- 10,10] Y = [- 14000,2000] C. X = [- 10,10] Y = [- 2000,14000] D. X = [- 10,10] Y = [0,9000] Estimate any relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.) B. There are no relative maxima. Estimate any relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.) B. There are no relative minima.

          Graph the function. Then estimate any relative extrema.
f(x) = -x^6 - 4x^5 + 54x^4 + 160x^3 - 641x^2 - 828x + 8,000
Graph the function. Choose the correct graph below.
A. X = [- 10,10] Y = [- 10000,10000]
B. X = [- 10,10] Y = [- 14000,2000]
C. X = [- 10,10] Y = [- 2000,14000]
D. X = [- 10,10] Y = [0,9000]
Estimate any relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.)
B. There are no relative maxima.
Estimate any relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.)
B. There are no relative minima.

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Graph the function. Then estimate any relative extrema.
f(x) = -x^6 - 4x^5 + 54x^4 + 160x^3 - 641x^2 - 828x + 8,000
Graph the function. Choose the correct graph below.
A. X = [- 10,10] Y = [- 10000,10000]
B. X = [- 10,10] Y = [- 14000,2000]
C. X = [- 10,10] Y = [- 2000,14000]
D. X = [- 10,10] Y = [0,9000]
Estimate any relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.)
B. There are no relative maxima.
Estimate any relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.)
B. There are no relative minima.

Added by Ronald H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

05/03/2023

Step 1

To do this, we will find the first derivative of the function and set it equal to 0. The function is: f(x) = -x^6 + 4x^5 + 54x^4 + 60x^3 + 641x^2 + 828x + 8000 Show more…

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Graph the function. Then estimate any relative extrema. f(x) = -x^6 - 4x^5 + 54x^4 + 160x^3 - 641x^2 - 828x + 8,000 Graph the function: Choose the correct graph below. X = [-10,10] Y = [-10000,10000] X = [-10,10] Y = [-14000,2000] X = [-10,10] Y = [-2000,14000] X = [-10,10] Y = [0,9000] Estimate any relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.) B. There are no relative maxima. Estimate any relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Round to three decimal places as needed. Use a comma to separate answers as needed. Type an ordered pair.) B. There are no relative minima.

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Transcript

00:01 So before starting this problem, i actually already knew that the correct answer for this graph of f of x based off of the first statement.

00:11 So the fact that you have a negative leading coefficient and an even degree, i knew that we had to choose the option that ended both down and to the left and down and to the right.

00:27 Because an even degree has the same in behavior and a negative is pointed down.

00:33 So from there, i went ahead and picked out the graph c and i finished typing out all this into my graph and calculator computer algebra system and saw the graph look exactly like what it does.

00:46 It goes up, down, up, down, and back up.

00:54 So in the second part of this question, so just so we're clear, question one, the answer is c.

01:04 With question two, there are several relative maxes.

01:10 There's three to be exact.

01:12 One, two, three.

01:15 And the way i interpret a max is i'm just going to give the y value and i'm going to go in order from least to greatest.

01:23 So i'm going to start with this one and i'm just typing into my calculator, second trace, the maximum.

01:30 A lot of computer algebra systems will do this and you just might have to enter a couple times on the left side, the right side, and in between.

01:37 And the values i got were, don't want the decimal in there, 10 ,013 .795.

01:47 And then do that again, same process, enter, enter, enter.

01:58 And the next time i got 88 ,240 .064.

02:07 Now if you're curious, oh, it does say type in ordered pairs.

02:12 So i probably should put that ordered pair in here, three decimals.

02:18 Kind of wish i gave myself some more room now...

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