Critical Number Problem - # 2

[Jason76]

Find Critical numbers for the given interval [-4.5]

\(\displaystyle 6x^{3} - 9x^{2} - 216x + 5\)

\(\displaystyle 18x^{2} - 18x - 216 + 5\)

\(\displaystyle 18x^{2} - 18x - 211\)

This factors out to imaginary numbers, so what are the critical values?

 

[Deleted member 4993]

Find Critical numbers for the given interval [-4.5]

\(\displaystyle 6x^{3} - 9x^{2} - 216x + 5\)

\(\displaystyle 18x^{2} - 18x - 216 + 5\) ...........................Incorrect

\(\displaystyle 18x^{2} - 18x - 211\)

This factors out to imaginary numbers, so what are the critical values?

.

 

[Jason76]

Find Critical numbers for the given interval [-4.5]

\(\displaystyle f(x) = 6x^{3} - 9x^{2} - 216x + 5\)

\(\displaystyle f'(x) = 18x^{2} - 18x - 216\)

\(\displaystyle 18x^{2} - 18x - 216 = 0\)

\(\displaystyle 18(x^{2} - x - 12) = 0\)

\(\displaystyle (x + 3)(x - 4) = 0\)

\(\displaystyle x = -3\)

\(\displaystyle x = 4\)

 

[Deleted member 4993]

Find Critical numbers for the given interval [-4.5]

\(\displaystyle f(x) = 6x^{3} - 9x^{2} - 216x + 5\)

\(\displaystyle f'(x) = 18x^{2} - 18x - 216\)

\(\displaystyle 18x^{2} - 18x - 216 = 0\)

\(\displaystyle 18(x^{2} - x - 12) = 0\)

\(\displaystyle (x + 3)(x - 4) = 0\)

\(\displaystyle x = -3\)

\(\displaystyle x = 4\)

Confused about what???

 

[Jason76]

Confused about what???

Computer homework says these answers are wrong.

 

[Jason76]

Find Critical numbers for the given interval [-4.5]

\(\displaystyle f(x) = 6x^{3} - 9x^{2} - 216x + 5\)

\(\displaystyle f(-4) = 6(-4)^{3} - 9(-4)^{2} - 216(-4) + 5 \)

\(\displaystyle f(-4) = 6(-64) - 9(-16) - 864 + 5 = \)

\(\displaystyle f(-4) = -384 - (-144) - 864 + 5 = \)

\(\displaystyle f(-4) = -384 + 144 - 864 + 5 = -1099\)

\(\displaystyle f(5) = 6(125) - 9(25) - 216(5) + 5 \)

\(\displaystyle f(5) = 725 - 225 - 1080 + 5 = -575\)

 

[lookagain]

Find Critical numbers for the given interval [-4.5]\(\displaystyle \ \ \ \ \)<---- Replace the period with a comma and make it "[-4, 5]."

\(\displaystyle f(x) = 6x^{3} - 9x^{2} - 216x + 5\)

\(\displaystyle f(-4) = 6(-4)^{3} - 9(-4)^{2} - 216(-4) + 5 \ \ \ \ \)

\(\displaystyle f(-4) = 6(-64) - 9(-16) - 864 + 5 = \ \ \ \ \)No. \(\displaystyle \ \ \)(-4)^2 = 16, not -16. \(\displaystyle \ \ \ \) And -216(-4) = + 864, not - 864.

\(\displaystyle f(-4) = -384 - (-144) - 864 + 5 = \)

\(\displaystyle f(-4) = -384 + 144 - 864 + 5 = -1099 \ \ \ \ \)Incorrect.



\(\displaystyle f(5) = 6(125) - 9(25) - 216(5) + 5 \)

\(\displaystyle f(5) = 725 - 225 - 1080 + 5 = -575 \ \ \ \ \ \)No. \(\displaystyle \ \ \)6(125) = 750, not 725.

.


f(-4) = -384 - 144 + 864 + 5 = 341

f(5) = 750 - 225 - 1080 + 5 = -550