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Neko [114]
3 years ago
11

Complete parts a through c for the given function.

Mathematics
2 answers:
victus00 [196]3 years ago
6 0

Answer:

a. The critcal points are at

x=0,-5,3

b. Then, x = -5   is a maximum and x=3 is a minimum

c. The absolute minimum is at   x = 3  and the absolute maximum is at  x = -5.

Step-by-step explanation:

(a)

Remember that you need to find the points where

f'(x)=0

Therefore you have to solve this equation.

20x^4  + 40x^3 - 300x^2 = 0

From that equation you can factor out    20x^2  and you would get

20x^2 (  x^2  +2x - 15)  = 0

And from that you would have   20x^2 = 0  , so x = 0.

And you would also have  x^2 +2x-15 = 0.

You can factor that equation as    x^2 +2x -15 = (x+5)(x-3) = 0

Therefore   x=-5 ,   x=3.

So the critcal points are at

x=0,-5,3

b.  

Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since

f''(x) = 80x^3 + 120x^2 -600x\\f''(-5) = 80(-5)^3 + 120(-5)^2 -600(-5) = -4000 < 0\\\\f''(3) = 80(3)^3 + 120(3)^2 -600(3) = 1440 > 0 \\

Then, x = -5   is a maximum and x=3 is a minimum

c.

The absolute minimum is at   x = 3  and the absolute maximum is at  x = -5.

son4ous [18]3 years ago
3 0

Answer:

(a) THE CRITICAL POINTS ARE (-5, 0, 3) on [-6, 4]

(b) THE LOCAL MINIMUM ARE AT

(-5, 3, 0), THERE ARE NO LOCAL MAXIMUM.

(c) THE ABSOLUTE MINIMUM IS -5

THE ABSOLUTE MAXIMUM IS 0.

(d) THE FUNCTION HAS NO EXTREMA.

Step-by-step explanation:

Given f(x) = 4x^5 + 10x^4 - 100x^3 - 4

We are required to find

(a) THE CRITICAL POINTS

The critical points are are the points where the first derivative vanishes.

That is the values x, where

f'(x) = 0

To find these points, let us differentiate f'(x) with respect to x

f'(x) = 20x^4 + 40x³ - 300x²

The points where f'(x) = 0 are the points where

20x^4 + 40x³ - 300x² = 0

20x²(x² + 2x - 15) = 0

x² = 0 => x = 0 is a point

The other points are

x² + 2x - 15 = 0

(x - 3)(x + 5) = 0

x = 3 and x = -5 are the remaining points.

THE CRITICAL POINTS ARE (-5, 0, 3) which are actually on [-6, 4]

(b) LOCAL MAXIMUM AND LOCAL MINIMUM

The Local Maximum is the critical point where the function is greater than zero, and the Local Minimum is the critical point where the function is less than zero.

f(x) = 4x^5 + 10x^4 - 100x^3 - 4

f(-5) = 4(-3125) + 10(625) + 100(-125)

= -15625 + 6250 - 12500 - 4

= -21879

f(0) = -4 < 0

f(3) = 4(243) + 10(81) - 100(27) - 4

= 972 + 810 - 2700 - 4

= -922 < 0

THE LOCAL MINIMUM ARE AT

(-5, 3, 0), THERE ARE NO LOCAL MAXIMUM.

(c) THE ABSOLUTE MINIMUM IS -5

THE ABSOLUTE MAXIMUM IS 0.

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Factor completely 3x3 − 6x2 − 24x. 3x(x − 4)(x + 2) 3x(x + 4)(x − 2) 3x(x − 3)(x − 2) 3x(x + 3)(x − 2)
inysia [295]

Answer:

3x(x - 4)(x + 2)

Step-by-step explanation:

Given

3x³ - 6x² - 24x ← factor out common factor of 3x from each term

= 3x(x² - 2x - 8) ← factor the quadratic

Consider the factors of the constant term (- 8) which sum to give the coefficient of the x- term.

The factors are - 4 and + 2, since

- 4 × 2 = - 8 and - 4 + 2 = - 2, thus

x² - 2x - 8 = (x - 4)(x + 2) and

3x³ - 6x² - 24x = 3x(x - 4)(x + 2)

7 0
3 years ago
Hey so im also looking for the first answer and the choices were “ is not “ and “ is “
dexar [7]

so the investigator found the skid marks were 75 feet long hmmm what speed will that be?

s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ d=75 \end{cases}\implies s=\sqrt{30(0.7)(75)}\implies s\approx 39.69~\frac{m}{h}

nope, the analysis shows that Charlie was going faster than 35 m/h.

now, assuming Charlie was indeed going at 35 m/h, then his skid marks would have been

s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ s=35 \end{cases}\implies 35=\sqrt{30(0.7)d} \\\\\\ 35^2=30(0.7)d\implies \cfrac{35^2}{30(0.7)}=d\implies 58~ft\approx d

4 0
2 years ago
What is 21/2 as a mixed number?
Daniel [21]
Since a fraction is a form of division, you do 21/2=10 and 1/2.
3 0
3 years ago
Read 2 more answers
What two simpler problem can you use to find 9×38?
elena55 [62]
Just a shot in the dark: 9*30 and 9*8?
8 0
3 years ago
Multiply to -260 add to 7
djyliett [7]
What can you be more specific like a put it in a sentence. For example x*-260+7=?

6 0
3 years ago
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