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lyudmila [28]
3 years ago
6

What is the average rate of change of the function fx= 2x2+ 3 over the interval [1,4]?

Mathematics
1 answer:
Molodets [167]3 years ago
6 0

Answer:

  10

Step-by-step explanation:

The average rate of change of f(x) on the interval [a, b] is found by ...

  m = (f(b) -f(a))/(b -a)

For your function, we have [a, b] = [1, 4}, so the rate of change is calculated as ...

  f(1) = 2·1² +3 = 5

  f(4) = 2·4² +3 = 35

  m = (35 -5)/(4 -1) = 30/3 = 10

The average rate of change on the interval is 10.

_____

<em>Comment on quadratic slope</em>

The slope of a quadratic curve changes continuously in linear fashion. The average slope on any interval is the slope at the midpoint of the interval. Using derivatives, we find the slope of the quadratic ax^2+bx+c to be given by 2ax+b. For the function given here, that is 4x. The midpoint of [1, 4] is x=2.5, so the slope at the midpoint is 4(2.5) = 10, as above.

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Consider the expression 16a + 4c.
kari74 [83]
The answer would -38
4 0
3 years ago
Boston , Massachusetts, and buffalo, New York, are hit by snowstorms that last 3 days . Boston accumulates snow at a rate of 1.5
stich3 [128]

Question is ;

Complete question is;

Boston , Massachusetts, and buffalo, New York, are hit by snowstorms that last 3 days . Boston accumulates snow at a rate of 1.5 feet every 36 hours. Buffalo accumulates snow at a rate of 0.01 inches every minute.

Which city accumulates more snow in 3 days? How much more snow?

Answer:

- Boston accumulates more snow in 3 days.

- It accumulates 0.6 ft of snow more than Boston

Step-by-step explanation:

Boston accumulates 1.5 feet of snow every 36 hours.

Number of hours in 3 days = 24 × 3 = 72 hours.

Thus, In 72 hours, Boston would have accumulated; (1.5 × 72)/36 = 3 feet of snow.

Now, Buffalo accumulates 0.01 inches of snow every minute.

In 3 days, number of minutes we have = 60 × 24 × 3 = 4320 minutes

Thus, total snow accumulated in 3 days = 0.01 × 4320/1 = 43.2 inches

Now, let's convert this to ft;

12 inches = 1ft

Thus; 43.2 inches = 43.2 × 1/12 = 3.6ft

Thus, Buffalo accumulates more snow in 3 days.

It accumulates 0.6 ft of snow more than Boston

3 0
3 years ago
a taxi service charges an initial fee of $5 plus $1.80 per mile. How many miles can you travel for $12
user100 [1]
First you need to write an equation or an inequality.

5+1.80x<=12 
the x here is how many miles you are paying for, now you just solve for x. 

5+1.80x<=12
-5                 -5

1.80x<=7
/1.80         /1.80
x<=3.8

you can travel only three whole miles, you do not have enough money to go four full miles.
4 0
3 years ago
Help me please ASAP!!!!
Alex

ummmmmm you dont need the explanation and I'd rather not type but trust me its d, good luck!

4 0
3 years ago
Read 2 more answers
Simplify 4y + 2y - 5y
goldfiish [28.3K]

Answer:

Your answer is y.

Step-by-step explanation:

4y+2y-5y         given

=6y-5y             add

=y                    subtract

5 0
3 years ago
Read 2 more answers
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