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3 years ago

F(x) = x4 - 32x2 + 7

1 answer:

4 0

F is increasing if f '(x) = 4x^3 - 64x >0, so it is the same of x(x^2 -16)>0, implies x>0 or (x-4)(x+4)>0, so x> + or -4
the answer is (-4 , 0) ∪ (4 , infinity)

f is decreasing if f '(x) = 4x^3 - 64x <0, so it is the same of x(x^2 -16)<0, implies x<0 or (x-4)(x+4)<0, so x< + or -4
the answer is (- infinity, -4) ∪ (0 , 4)

the local minimum and maximum
f '(x) =0, impolies x=+ or -4, or x=0
or f'(o)=0, and f'(- 4)=f'(4)= 0,
M(-4, 0) or M(4, 0) or M(0,0)

inflection points can be found by solving f '' (x)=12x^2 - 64 =0
x=+ or - 4sqrt(3) / 3
so the inflection point is and M(- 4sqrt(3) / 3, f'' ( -4sqrt(3)) (smaller x value), and M(4sqrt(3) / 3, f'' (4sqrt(3)) (larger x value)

f is concave up if f ''>0
it means 12x^2 - 64>0, so the interval is (- infinity, -4sqrt(3) U (4sqrt(3), infinity)

f is concave down if f ''<0
it means 12x^2 - 64<0 so the interval is (-4sqrt(3)) U (4sqrt(3))

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I need help on this.

SSSSS [86.1K]

Answer:

plot the first point on (0,-4)

from there, rise 2, then run 3

plot another point on (3,-2)

plot another on (6,0), and so on

Plz mark as brainliest if correct! Have a nice day!!! 

-Lil G

8 0

3 years ago

rachel was cutting out some fabric for a friend. she cut a piece that was 5 cm wide and had an area of 20(20)cm. how long was th

Pavlova-9 [17]

Area of a rectangle is L * W

L = x
W = 5

5x = 20 (Divide by 5 on both sides)
x = 4

L=4
W= 5

The length is 4cm

Hope this helps :)

3 0

3 years ago

Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

3 years ago

Write an example of a trinomial that cannot be factored.

OverLord2011 [107]

Answer:

$x^{2} + x + 1$

Step-by-step explanation:

a trinomial that cannot be factored has no real roots.

here is one:

$x^{2} + x + 1$

After graphing this trinomial has no intersections points with the x-axis wich means it has no roots

5 0

3 years ago

1.1 solve for x, where 0°< x 90°. write your answer to one decimal place. 1.1.1 tanx=sin38° 1.1.2cosec( x+10°)=1.345

snow_lady [41]

The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0

<h3>How to solve the trigonometry ratios?</h3>

The equations are given as:

tan(x)=sin38°

cosec( x+10°)=1.345

In tan(x)=sin38°, we have:

tan(x)=0.6157

Take the arc tan of both sides

x = 31.6

Also, we have:

cosec(x+10°)=1.345

Take the inverse of both sides

sin(x+10°) = 0.7434

Take the arc sin of both sides

x+10 = 48.0

Subtract 10 from both sides

x = 38.0

Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0

Read more about trigonometry ratios at:

brainly.com/question/11967894

#SPJ1

5 0

2 years ago