Use the conversions given below to change 127 cm into feet

Given a function f(x)=2x^2+3, what is the average rate of change of f on the interval [2, 2+h]?

AveGali [126]

Answer:

4x+2h

Step-by-step explanation:

The average rate of change of a continuous function,

f

(

x

)

, on a closed interval

[

a

,

b

]

is given by

f

(

b

)

−

f

(

a

)

b

−

a

So the average rate of change of the function

f

(

x

)

=

2

x

2

+

1

on

[

x

,

x

+

h

]

is:

A

r

o

c

=

f

(

x

+

h

)

−

f

(

x

)

(

x

+

h

)

−

(

x

)

=

f

(

x

+

h

)

−

f

(

x

)

h

...

.

[

1

]

=

2

(

x

+

h

)

2

+

1

−

(

2

x

2

+

1

)

h

=

2

(

x

2

+

2

x

h

+

h

2

)

+

1

−

2

x

2

−

1

h

=

2

x

2

+

4

x

h

+

2

h

2

−

2

x

2

h

=

4

x

h

+

2

h

2

h

=

4

x

+

2

h

Which is the required answer.

Additional Notes:

Note that this question is steered towards deriving the derivative

f

'

(

x

)

from first principles, as the definition of the derivative is:

f

'

(

x

)

=

lim

h

→

0

f

(

x

+

h

)

−

f

(

x

)

h

This is the function we had in [1], so as we take the limit as

h

→

0

we get the derivative

f

'

(

x

)

for any

x

, This:

f

'

(

x

)

=

lim

h

→

0

4

x

+

2

h

=

4

x

4 0

3 years ago

Jo said that when you multiply a nonzero whole number by a fraction less than 1, the product is always less than the whole numbe

tiny-mole [99]

Answer:

Jo is correct.

Step-by-step explanation:

No matter what number you multiply by, a fraction between 0 and 1 will give you less than the original whole number.

4 0

4 years ago

F(x) = -3x + 7 x = -2

Marat540 [252]

Answer:

X= 1/2

Step-by-step explanation:

-3x+7x=2

4x = 2

4x/4 + 2/4

X= 1/2

8 0

3 years ago

Read 2 more answers

If h(2)=7 and h'(2)=-2,find d/dx [(h(x))/(x)] <br> A. –11/4 B. 2 C. D. 8 E. 16

valentinak56 [21]

Answer:

A. $\frac{-11}{4}$

Remember that if f and g are functions with $g(x)\neq 0$ then, $\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2}$ .

Then,

$\frac{d}{dx}\frac{h(x)}{x}=\frac{h'(x)x-h(x)}{x^2}$

Evaluating in x=2,

$\frac{h'(2)*2-h(2)}{2^2}=\frac{-4-7}{4}=\frac{-11}{4}$

Then the answer is A.

7 0

4 years ago

A survey of 73 college students was taken to determine the musical styles they liked. Of those, 27 students listened to rock,

vovangra [49]

Attached is a Venn diagram of your problem.

Knowing how many likes all three will help. You know that 10 students like all three.

Rock and Jazz only:
16 like rock and jazz while 10 like all three. To get how many like jazz only, subtract 10 from 16.

16-10 = 6

Rock and Classical only:
13 like rock and classical while 10 like all three. To get how many like jazz only, subtract 10 from 13.

13-10 = 3

Jazz and classical only:
12 like jazz and classical while 10 like all three. To get how many like jazz only, subtract 10 from 12.

12-10 = 2

Now with that data you fill up the 4 intersecting areas. To get the outer, just remember that all areas within a circle should add up to the first assumption.
27 rock
24 classical
28 Jazz

All numbers in the rock circle should add up to 27.
All numbers in the classical circle should add up to 24.
All numbers in the Jazz circle should add up to 28.

Rock:
3+10+6+x = 27
19+x=27
x = 27-19
x= 8

Classical:
3+10+2+x = 24
15 + x = 24
x = 24-15
x = 9

Jazz:
10+6+2+x = 28
18 + x = 28
x = 28 - 18
x = 10

In summary: 8 liked only Rock, 9 liked only Classical, 10 liked only Jazz.

7 0

3 years ago