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2 years ago

Use the four-step definition of the derivative to find f'(x) if f(x) = −4x^3 −1.

1 answer:

7 0

$\stackrel{de finition \textit{ of a derivative as a limit}}{\lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[-4(x+h)^3-1]~~ - ~~[-4x^3-1]}{h} \\\\\\ \cfrac{[-4(x^3+3x^2h+3xh^2+h^3)-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{[-4x^3-12x^2h-12xh^2-4h^3-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{-4x^3-12x^2h-12xh^2-4h^3-1+4x^3+1}{h}\implies \cfrac{-12x^2h-12xh^2-4h^3}{h}$

$\cfrac{h(-12x^2-12xh-4h^2)}{h}\implies -12x^2-12xh-4h^2 \\\\\\ \lim\limits_{h\to 0}~-12x^2-12xh-4h^2\implies \lim\limits_{h\to 0}~-12x^2-12x(0)-4(0)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \lim\limits_{h\to 0}~-12x^2~\hfill$

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Is 30/12 and 40/16 equivalent?

Flura [38]

30/12 in simplest form is 5/2 (cause 6 * 5 = 30 and 6 * 2 = 12)
40/16 in simplest form is 5/2 (cause 8 * 2 = 16 and 8 * 5 =40)
so yes they're equivalent;
30/12 = 40/16
Hope that helps :D have a nice day!

5 0

3 years ago

Read 2 more answers

A standard die (a six-sided cube with the numbers 1‚ 2‚ 3‚ 4‚ 5‚ and 6 on the sides) is rolled 150 times. Which of the following

Mama L [17]

Answer:

Step-by-step explanation:

1÷6×150=25

ans:25+25

=50

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3 years ago

2.The number of tickets sold to a play for each showing is 78, 84, 87, 80, 91, 95, and 80.

Luden [163]

Answer:

$Min =78$

The maximum is :

$Max = 95$

Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:

$Median =84$

Now we can find the quartile 1 we analyze the first 4 values 78, 80,80, 84 and the first quartile would be:

$Q_1= \frac{80+80}{2}= 80$

Now we can find the quartile 3 we analyze the last 4 values 84,87, 91, 95 and the third quartile would be:

$Q_3= \frac{87+91}{2}=89$

And finally the 5 number summary would be:

$Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96$

Step-by-step explanation:

We have the following data given:

78, 84, 87, 80, 91, 95, and 80.

The first step is order the dataset on increasing way and we got:

78, 80,80, 84,87, 91, 95

We can begin finding the minimum value and for this case is:

$Min =78$

The maximum is :

$Max = 95$

Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:

$Median =84$

Now we can find the quartile 1 we analyze the first 4 values 78, 80,80, 84 and the first quartile would be:

$Q_1= \frac{80+80}{2}= 80$

Now we can find the quartile 3 we analyze the last 4 values 84,87, 91, 95 and the third quartile would be:

$Q_3= \frac{87+91}{2}=89$

And finally the 5 number summary would be:

$Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96$

5 0

3 years ago

The division sign and the capital letter "T", is there any rotational symmetry and how so?

kirill115 [55]

Answer:

Rotational symmetry 1

Step-by-step explanation:

You will get only one rotational symmetry when you turn 360

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3 years ago

Find the greatest common factor (GCF) of the set of numbers.<br><br><br> 21, 30, 44

Vitek1552 [10]

Step-by-step explanation:

Answer attached :)

Hope it helps :D

7 0

3 years ago