Answer:
20 1/3
Explanation:
5/10=1/2
4/12=1/3
3/9=1/3
6/9=2/3
2/16=1/8
10/40=1/4
2/4=1/2
6/18=1/3
4/20=1/5
9/27=1/3
7/27---- something wrong with this
8/36=2/9
Critical points: (Maximum, minimum, and inflection points) have a slope = 0
The derivative gives the slope, take the derivative set it equal to zero
<span>f(x) = x^5 -10x^3 + 9x
derivative:
f'(x) = 5x^4 - 30x^2 + 9
0 = 5x^4 - 30x^2 + 9
use quadratic formula (or polysolver) with a=5, b=-30 and c = 9
4th degree gives 4 solutions
x = +/- √(3 - 6/√(5))
x ~ +/- 2.38
x = +/- √(3 - 6/√(5))
x ~ +/- 0.563
</span>Determine which point is the highest (maximum) and the lowest (minimum) by putting the x-coordinates back into the original equation and comparing y-values.
* You will also need to check the endpoints given as these can sometime be the max/min of the function.
Our x-values:
x = { -3, -2.38, -0.563, 0.563, 2.38, 3}
respective y-values found by inputting x's into function
y = {0, 37.03, -3.34, 3.34, -37.03, 0}
nice symmetry.. check out the graph to see the solutions are correct.
https://www.desmos.com/calculator
Maximum point (-2.38, 37.03)
Minimum point (2.38, -37.03)
<span>-x^2 - 4x when x = -3
-(-3)^2 -4(-3)
= - 9 + 12
= 3
answer is </span><span>B. 3 </span>