2mx?x3m=24m3 help plsssssss!!!!!!!!!!!!!!!!

Find all critical numbers of the function <img src="https://tex.z-dn.net/?f=g%28x%29%3Dx%5E%7B%5Cfrac%7B3%7D%7B4%7D%20%7D-2x%5E%

postnew [5]

Differentiate g using the power rule:

$g'(x) = \dfrac34 x^{\frac34-1} - 2\cdot\dfrac14 x^{\frac14-1}$

$g'(x) = \dfrac34 x^{-\frac14} - \dfrac12 x^{-\frac34}$

$g'(x) = \dfrac14 x^{-\frac34} \left(3 x^{\frac12} - 2\right)$

$g'(x) = \dfrac{3\sqrt x - 2}{4 x^{\frac34}}$

The critical points of g occur where g' is zero or undefined.

We have

$g'(x) = 0 \implies 3\sqrt x - 2 = 0 \implies \sqrt x = \dfrac23 \implies \boxed{x = \dfrac49}$

and the derivative is undefined for

$\dfrac1{g'(x)} = 0 \implies 4x^{\frac34} = 0 \implies \boxed{x=0}$

8 0

3 years ago

the first four terms in an arithmetic sequence are $x y$, $x - y$, $xy$, and $x/y$, in that order. what is the fifth term?

olga2289 [7]

When the first four terms in an arithmetic sequence are x+y, x-y, xy and x÷y, then the fifth term will be $\frac{123}{40}$

A sequence of numbers in which every term (except the first term) is obtained by adding a constant number to the previous term is called an arithmetic sequence

In given arithmetic sequence

The first term = x+y

The second term = x-y

Then, the common difference= (x-y)-(x+y)

x-y-x-y= -2y

The third term = x-y+(-2y)

x-y-2y= x-3y

In question third term is given as xy

So both are equal

x-3y=xy

-3y=xy-x

-3y=x(y-1)

x= $\frac{-3y}{y-1}$

Similarly fourth term will be

x-3y-2y=x-5y

$x-5y=\frac{x}{y}$

substitute the value of x in the equation

$\frac{-3y}{y-1}-5y=\frac{\frac{-3y}{y-1} }{y} \\\frac{-3y}{y-1} -5y=\frac{-3}{y-1}\\ -3y-5y(y-1)=-3\\-3y-5y^{2}+5y=-3\\ -5y^{2} +2y+3=0\\5y^{2} -2y-3=0$

Split the middle term and factorize it

$5y^{2}+3y-5y-3=0\\y(5y+3)-1(5y+3)=0\\$

(y-1)(5y+3)=0

$y=1,\frac{-3}{5}$

y cannot be equal to 1, because the third term and fourth term will become x.

$y=\frac{-3}{5}$

substitute the value of y in the equation of x
$x=\frac{-3y}{y-1} \\=\frac{-3\frac{-3}{5} }{\frac{-3}{5}-1 }\\ =\frac{-9}{8}$

The fifth term= $\frac{x}{y}+(-2y)=\frac{x}{y} -2y$

$\frac{\frac{-9}{8} }{\frac{-3}{5} }-2\frac{-3}{5} =\frac{123}{40}$

Hence, when the first four terms in an arithmetic sequence are x+y, x-y, xy and x÷y, then the fifth term will be $\frac{123}{40}$

Learn more about Arithmetic sequence here

brainly.com/question/15412619

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5 0

2 years ago

Use the order of operations to evaluate the expression below. 6 +5•8-80/4-3-3

11Alexandr11 [23.1K]

Answer:

20

Step-by-step explanation:

6 + 5 × 8 - 80 ÷ 4 - 3 - 3

Step 1 (multiply 5 x 8)

Step 2 (divide 80÷5)

Step 4 (add 6 + 40)

Step 5 (subtract 46-20)

Step 6 (subtract 26-3-3)

Which then leaves you with 20

Hope this helped!

:)

7 0

3 years ago

Here are Janet's steps for solving the system below by eliminating x.

Lunna [17]

2x + 3y = -1.....(5)
5x + 8y = 0.....(-2)
-----------------------
10x + 15y = -5
-10x - 16y = 0
-----------------------add
-y = -5
y = 5 <=====this is where Janet messed up

2x + 3y = -1
2x + 3(5) = -1
2x + 15 = -1
2x = -1-15
2x = -16
x = -16/2
x = - 8

solution is : (-8,5)

7 0

3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! I CANNOT RETAKE THIS!!

jonny [76]

Answer: x = {-3, -1, 1, 7}

Step-by-step explanation:

f(x) = x⁴ - 4x³ - 22x² + 4x + 21

possible roots are: +/- 1, 3, 7, 21

Let's try x = 1

1 | 1 -4 -22 4 21

| ↓ 1 -3 -25 -21

1 -3 -25 -21 0 remainder is 0 so (x - 1) is a factor

(x - 1)(x³ - 3x² - 25x - 21)

Next, let's try x = -1

-1 | 1 -3 -25 -21

| ↓ -1 4 21

1 -4 -21 0 remainder is 0 so (x + 1) is a factor

(x - 1)(x + 1)(x² - 4x - 21)

Then, factor the third polynomial

(x - 1)(x + 1)(x + 3)(x - 7)

Now, set each factor equal to zero and solve each one.

(x - 1) = 0 ⇒ x = 1

(x + 1) = 0 ⇒ x = -1

(x + 3) = 0 ⇒ x = -3

(x - 7) = 0 ⇒ x = 7

6 0

4 years ago

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