Divide.

For each of the terms below, give a brief definition.

irinina [24]

Answer:

term

a word or phrase used to describe a thing

Coefficient

a number for constant quantity

constant

occurring continuously over a period of time

Algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

5 0

3 years ago

Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter

Vaselesa [24]

We have been given a function $f(x)=2x^3+3x^2-336x$ . We are asked to find the interval on which function is increasing and decreasing.

(a). First of all, we will find the critical points of function by equating derivative with 0.

$f'(x)=2(3)x^{2}+3(2)x^1-336$

$f'(x)=6x^{2}+6x-336$

$6x^{2}+6x-336=0$

$x^{2}+x-56=0$

$x^{2}+8x-7x-56=0$

$(x+8)-7(x+8)=0$

$(x+8)(x-7)=0$

$x=-8,x=7$

So $x=-8,7$ are critical points and these will divide our function in 3 intervals $(-\infty,-8)U(-8,7)U(7,\infty)$ .

Now we will find derivative over each interval as:

$f'(x)=(x+8)(x-7)$

$f'(-9)=(-9+8)(-9-7)=(-1)(-16)=16$

Since $f'(9)>0$ , therefore, function is increasing on interval $(-\infty,-8)$ .

$f'(x)=(x+8)(x-7)$

$f'(1)=(1+8)(1-7)=(9)(-6)=-54$

Since $f'(1)$ , therefore, function is decreasing on interval $(-8,7)$ .

Let us check for the derivative at $x=8$ .

$f'(x)=(x+8)(x-7)$

$f'(8)=(8+8)(8-7)=(16)(1)=16$

Since $f'(8)>0$ , therefore, function is increasing on interval $(7,\infty)$ .

(b) Since $x=-8,7$ are critical points, so these will be either a maximum or minimum.

Let us find values of f(x) on these two points.

$f(-8)=2(-8)^3+3(-8)^2-336(-8)$

$f(-8)=1856$

$f(7)=2(7)^3+3(7)^2-336(7)$

$f(7)=-1519$

Therefore, $(-8,1856)$ is a local maximum and $(7,-1519)$ is a local minimum.

(c) To find inflection points, we need to check where 2nd derivative is equal to 0.

Let us find 2nd derivative.

$f''(x)=6(2)x^{1}+6$

$f''(x)=12x+6$

$12x+6=0$

$12x=-6$

$\frac{12x}{12}=-\frac{6}{12}$

$x=-\frac{1}{2}$

Therefore, $x=-\frac{1}{2}$ is an inflection point of given function.

3 0

2 years ago

What is the value of the expression shown below?

Ymorist [56]

(8 + [7+1] 2 ÷ 4 × 1) ÷ 2^4

Let's focus on what's in parentheses first.

8 + 8 × 2 ÷ 4 × 1
8 + 16 ÷ 4 × 1
8 + 4 × 1
8 + 4
12

Now, to what is outside the parentheses:

Because of the way it is written, you will do 12 ÷ 2 first.
12 ÷ 2^4
6^4

Answer: 1296

8 0

2 years ago

Read 2 more answers

What is the base of the expression 11^12? 3 11 12 21

Sever21 [200]

Answer:

An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent

therefore, the correct answer is 11

5 0

3 years ago

Read 2 more answers

X+x+x+2 which are equivalent

kodGreya [7K]

3x+2 is the simplest equivalent answer

7 0

3 years ago