$\{x|x\in\mathbb{N}\ \wedge\ n < 10\}=\{0;\ 1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9\}-FINITE\\\\\{x|x\in\mathbb{Z}\ \wedge\ 0 < x < 10\}=\{1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9\}-FINITE\\\\\{x|x\in\mathbb{Z}\ \wedge\ x < 0\}=\{...;-4;-3;-2;-1\}=\mathbb{Z}^--NOT\ FINITE$

8 0

3 years ago

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE

Viktor [21]

Answer:

Step-by-step explanation:

Given the function f(x) = 8x³ − 12x² − 48x, <em>the critical point of the function occurs at its turning point i,e at f'(x) = 0</em>

First we have to differentiate the function as shown;

$f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\ \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\$

$Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1$

Hence the critical numbers of the function are (2, -1)

8 0

3 years ago

Carly is ordering candles online.

kirza4 [7]

Answer:

Is that the whole question or....

7 0

3 years ago

What are some of the applications for exponential functions?

frozen [14]

Answer:

Some of the applications for exponential functions are:

1. model populations

2. carbon date artifacts

3. compound interest

hope this helps!

4 0

3 years ago