In case you're not already aware, the expression $\frac{f(x+h)-f(x)}h$ is called the "difference quotient" and represents the average rate of change of a function $f$ over an interval $[x,x+h]$ .

For the function $f(x)=x^2+3x+4$ , by substituting $x+h$ we get

$f(x+h)=(x+h)^2+3(x+h)+4=(x^2+2xh+h^2)+(3x+3h)+4=x^2+3x+4+(2x+3)h+h^2$

Then the difference quotient is

$\dfrac{f(x+h)-f(x)}h=\dfrac{(x^2+3x+4+(2x+3)h+h^2)-(x^2+3x+4)}h$

$=\dfrac{(2x+3)h+h^2}h=2x+3+h$

where the last equality holds as long as $h\neq0$ .

5 0

3 years ago

Paul bought 9 total shirts for a total of 72 tee shirts cost 10 and long sleeve shirts cost 7. how many of each shirt did he buy

FinnZ [79.3K]

6 long sleeve and 3 short sleeves.

8 0

3 years ago

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What is the length of one side of a cube that has a surface area of 1,734 square mm?

jarptica [38.1K]

Answer:

a = 17

Step-by-step explanation:

1,734 = 6a^2

1,734/6 = 6a^2/6

$\sqrt{289}$ = $\sqrt{a^2}$

a = 17

7 0

3 years ago

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a cell phone company offers two different monthly plans.plan a charges $41 for unlimited cell phone minutes plus $0.10 per text

tiny-mole [99]

41+0.10x = 31+0.15x

10 +0.10x=0.15x

10=0.05x

x=10/.05

x= 200 text messages

check 200*0.10 = 20 +41 =61

200*0.15 = 30+31 = 61

they equal each other so number of texts is 200

6 0

3 years ago