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Tcecarenko [31]

3 years ago

13

A number n is at least 4

1 answer:

s344n2d4d5 [400]3 years ago

3 0

n<span>≥4
</span><span>≥ is the sign for least. It means greater than or equal to as well.
</span>
Hope this helps :)

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Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify

irina [24]

Answer:

x-coordinates of relative extrema = $\frac{-1}{2}$

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

$f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}$

Differentiate with respect to x

$f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}$

$f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}$

Differentiate f'(x) with respect to x

$f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1$

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

$f''\left ( \frac{-1}{2} \right )=\frac{4\left ( -1+4\left ( \frac{-1}{2} \right ) \right )}{3\left ( \frac{-1}{2} \right )^{\frac{5}{3}}}>0$

We know that if $f''(a)>0$ then x = a is a point of minima.

So, $x=\frac{-1}{2}$ is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

7 0

3 years ago

SOLVE THE CORRECT ANSWER!

UNO [17]

Step-by-step explanation:

1.

123445+(89-23765)=99769

2.

234.57+(5.23-2.678)=237.122

3

(21.54+ 80.27)-68.501=33.309

5 0

3 years ago

In rectangle ABCD, if the coordinates of A are (0, 0) and of C are (r, s), find the coordinates of B and D.

goldenfox [79]

Answer:

Answers are (r,0) and (0,s)

Step-by-step explanation:

Given that in a rectangle ABCD, one vertex is the origin (0,0) A

The opposite vertex C is having coordinates as (r,s)

Since a rectangle has angle 90 we have x axis as one side and y axis as other side.

Length = r and width =s (since coordinates of C are (r,s))

Hence other coordinate B on x axis would be = (r,0)

and D on y axis = (0,s)

Answers are (r,0) and (0,s)

3 0

3 years ago

Read 2 more answers

to play at a bingo night,there is a $10 cover charge,plus $2 per bingo card .Write a equation for the cost (y) based on the numb

Aleksandr [31]

Y=2x+10

That is the eqasion, 2(it is the cost per card) and multpy be how many cards you want, then add 10 as base fee

3 0

3 years ago

What kind of sequence is this? 1, 8, 64, 512, ...<br> arithmetic, geometric, neither or both

MatroZZZ [7]

Answer:

Geometric

Step-by-step explanation:

It has a consistent multiple-factor by which it increases (8).

7 0

3 years ago