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damaskus [11]
3 years ago
13

Find the local max and min values of f(x)=x^2/x-1 using both first and second derivative tests

Mathematics
1 answer:
uranmaximum [27]3 years ago
6 0
Hmm, the 2nd derivitve is good for finding concavity

let's find the max and min points
that is where the first derivitive is equal to 0
remember the difference quotient

so
f'(x)=(x^2-2x)/(x^2-2x+1)
find where it equals 0
set numerator equal to 0
0=x^2-2x
0=x(x-2)
0=x
0=x-2
2=x

so at 0 and 2 are the min and max
find if the signs go from negative to positive (min) or from positive to negative (max) at those points

f'(-1)>0
f'(1.5)<0
f'(3)>0

so at x=0, the sign go from positive to negative (local maximum)
at x=2, the sign go from negative to positive (local minimum)


we can take the 2nd derivitive to see the inflection points
f''(x)=2/((x-1)^3)
where does it equal 0?
it doesn't
so no inflection point
but, we can test it at x=0 and x=2
at x=0, we get f''(0)<0 so it is concave down. that means that x=0 being a max makes sense
at x=2, we get f''(2)>0 so it is concave up. that means that x=2 being a max make sense




local max is at x=0 (the point (0,0))
local min is at x=2 (the point (2,4))
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7 0
3 years ago
If a dozen eggs cost $1.35, what is the unit cost?
Ulleksa [173]
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4 0
3 years ago
A geologist visits 40 volcanoes in Alaska and California.how many volcanoes does the geologist visit in California and how many
solong [7]

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

Answer:

I don't know for sure, but there are a bunch of different options. Here they are:

Step-by-step explanation:

1 + 39

2 + 38

3 + 37

4 + 36  

5 + 35

6 + 34

7 + 33

8 + 32

9 + 31

10 + 30

11 + 29

12 + 28

13 + 27

14 + 26

15 + 25

16 + 24

17 + 23

18 + 22

19 + 21

20 + 20

Those are the options of how many volcanoes that they could have visited. They could have visited 23 volcanoes in Alaska and 17 in California. Who knows?

California only has 20 volcanoes, and Alaska has 40, so your answer will be one of these options. Hope this helps!

5 0
3 years ago
Car A, traveling at a constant 10 m/s, crosses the start line 3 seconds before Car B, who is traveling at a constant 15 m/s. At
Margaret [11]
The distance between Car A and car B,When Car A crosses the start line is:
distance =speed car B* time
distance=(15 m/s)(3 s)=45 m
 
Distance traveled by car A =x,  (when the car B is at the same distance from the start line)
time of car A=t

x=10 m/st  ⇒    x=10t    (1)

Distance traveled by car B=x
time of car B=t-3

x=15(t-3)  (2)

With the equations (1) and (2) we make a system of equations:

x=10t
x=15(t-3)

We solve this system of equations:

10t=15(t-3)
10t=15t-45
-5t=-45
t=-45 / -5
t=9

t-3=9-3=6

x=10 t=10 (9)=90

Answer: The time would be 9 seconds for Car A and 6 seconds for car B and the distance would be 90 meters.
8 0
3 years ago
In 1935, there were 15,295 banks in the United States. In 2003 there were 9,182 banks. What is the percent of the change? Is it
Sati [7]
If it goes from a higher number to a lower number it is a decrease.

(15,295 - 9182) / 15295....x 100
6113 / 15295 = 0.399....x 100 = 39.9% decrease

5 0
3 years ago
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