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motikmotik
3 years ago
5

Find the intervals on which the function is increasing or decreasing.

Mathematics
1 answer:
Assoli18 [71]3 years ago
6 0
To solve this, you have to know that the first derivative of a function is its slope. When an interval is increasing, it has a positive slope. Thus, we are trying to solve for when the first derivative of a function is positive/negative.

f(x)=2x^3+6x^2-18x+2
f'(x)=6x^2+12x-18
f'(x)=6(x^2+2x-3)
f'(x)=6(x+3)(x-1)
So the zeroes of f'(x) are at x=1, x=-3
Because there is no multiplicity, when the function passes a zero, he y value is changing signs.
Since f'(0)=-18, intervals -3<x<1 is decreasing(because -3<0<1)
Thus, every other portion of the graph is increasing.
Therefore, you get:

Increasing: (negative infinite, -3), (1, infinite)
Decreasing:(-3,1)
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A group of artists is selling small prints to raise money for charity. They sell p prints, and make a profit of f(p) on the sale
MrRissso [65]

Answer:

Statement A is true.

Step-by-step explanation:

A. If the group sells 15 prints, they will lose $85.

B. If the group sells 12 prints, they will lose $204.

C. If the group sells 35 prints, they will make $935.

D. If the group sells 28 prints, they will lose $136.

f(p) = 17p - 340

p = prints

f(p) = profit

Let's check the statements to see which one is true.

A. 17.15 - 340 = - 85 OK!

B. 17.12 - 340 = -136 (false, they will lose $136)

C. 17.35 - 340 = 255 (false, they will make $255)

D. 17.28 - 340 = 136 (false, they will make $136)

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3 years ago
What is your estimate for the number of airline flights in a year?
Firdavs [7]
The answer is between 45,000,000-65,000,000
8 0
3 years ago
The area of a circle is equal to 1 dm2. Find the radius of the circle.
lisov135 [29]

Answer:

2000

Step-by-step explanation:

1 dm =1000

2dm =?

2dm x 1000

1dm

2000

7 0
2 years ago
Answers with links will be reported
Ber [7]

Answer:

11 months

Step-by-step explanation:

the math that i did was i kept adding 400 to 2500 and counted every four hundred that i added witch was 11 until i got to 7000 so the answer is 11 months. You will have some left over which you will have 300 left over.

8 0
3 years ago
Nevaeh invested $660 in an account paying an interest rate of 3% compounded
iris [78.8K]

Answer:

19

Step-by-step explanation:

Rate 1: 3  

4

1

​  

%=3+1/4=

\,\,3.25\%\rightarrow 0.0325

3.25%→0.0325

\text{Rate 2: }3\tfrac{1}{8}\%=3+1/8=

Rate 2: 3  

8

1

​  

%=3+1/8=

\,\,3.125\%\rightarrow 0.03125

3.125%→0.03125

\text{Calculate Final Amount for Nevaeh}

Calculate Final Amount for Nevaeh

\overline{\phantom{\text{Calculate Final Amount for Nevaeh}}}

Calculate Final Amount for Nevaeh

 

\text{Compounded Continuously:}

Compounded Continuously:

A=Pe^{rt}

A=Pe  

rt

 

P=660\hspace{35px}r=0.0325\hspace{35px}t=14

P=660r=0.0325t=14

Given values

A=660e^{0.0325(14)}

A=660e  

0.0325(14)

 

Plug in

A=660e^{0.455}

A=660e  

0.455

 

Multiply

A=1040.2744

A=1040.2744

Use calculator (with e button)

\text{Calculate Final Amount for Jonathan}

Calculate Final Amount for Jonathan

\overline{\phantom{\text{Calculate Final Amount for Jonathan}}}

Calculate Final Amount for Jonathan

 

\text{Compounded Monthly:}

Compounded Monthly:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+  

n

r

​  

)  

nt

 

Compound interest formula

P=660\hspace{35px}r=0.03125\hspace{35px}t=14\hspace{35px}n=12

P=660r=0.03125t=14n=12

Given values

A=660\left(1+\frac{0.03125}{12}\right)^{12(14)}

A=660(1+  

12

0.03125

​  

)  

12(14)

 

Plug in values

A=660(1.0026042)^{168}

A=660(1.0026042)  

168

 

Simplify

A=1021.6468

A=1021.6468

Use calculator

\text{How much more money Nevaeh has:}

How much more money Nevaeh has:

1040.2744-1021.6468

1040.2744−1021.6468

18.6276

18.6276

\$ 19

$19

4 0
2 years ago
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