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3 years ago

Find the derivative of f(x) = (1 + 6x2)(x − x2) in two ways.

1 answer:

3 0

Using product rule;

f(x)=(1+6x²)(x-x²)

f'(x)=(12x)(x-x²) + (1-2x)(1+6x²) = 12x² -12x³ +1 +6x² -2x -12x³ = -24x³ +18x² -2x +1

Solving the bracket first;

f(x)=(1+6x²)(x-x²) = x -x² +6x³ -6x^4

f'(x)= 1 -2x +18x² -24x³ = -24x³ +18x² -2x +1

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Help ASAP!!<br>Using the graphed function above, find the following

Alenkinab [10]

Answer:

Maximum: 1, Minimum: -3, Midline y = -1, Amplitude = 4, Period = $\pi$ , Frequency $\displaystyle =\frac{1}{\pi}$ , equation : $f(x)=-4cos(2x)+1$

Step-by-step explanation:

<u>Sinusoid Functions</u>

It refers to the oscillating functions like the sine or cosine which range from a minimum and maximum value periodically.

The graph shown can give us all the information we need to answer these questions:

Maximum: 1

Minimum: -3

The midline goes through the center value (mean) of the max and min values, i.e.

Equation of the midline:

$\displaystyle y=\frac{1-3}{2}=-1$

Amplitude is the difference between the maximum and minimum values

$A=1-(-3)=4$

The period is the time it takes to complete a cycle. We can see the minimum value is first reached at x=0 and next at $x=\pi$

Thus the period is

$T=\pi$

The frequency is the reciprocal of the period:

$\displaystyle f=\frac{1}{T}=\frac{1}{\pi}$

The angular frequency is

$\displaystyle w=2\pi f=\frac{2\pi }{\pi}=2$

The equation of the function is a negative cosine (since it starts at the minimum) or a shifted sine or cosine. We'll choose the negative cosine, knowing all the parameters:

$f(x)=-4cos(2x)+1$

5 0

3 years ago

Explain how you use a quick picture to find the quotient and remainder

Varvara68 [4.7K]

Example question: There are 38 students in a baseball club. The coach needs to split them up into equal groups of 4. How many groups can be made? How many kids are left over?
Answer: You would make groups of 4 to get your quotient (9). Then whatever is NOT in a group is your left over.

8 0

4 years ago

Read 2 more answers

Which of the following equations has the given solution set?

tester [92]

-2m + 5 = 2m + 5
2m + 2m = 5 - 5
4m = 0
m = 0

-2m + 5 = -2m + 5
-2m + 2m = 5 - 5
0 = 0

-2m + 5 = -2m - 5
-2m + 2m = 5 + 5
0 = 10
Solution set is Ф
The third equation is the correct answer.

8 0

3 years ago

If the two legs of an isosceles right triangle measure 7 in which of the following represents the length of its hypotenuse

anyanavicka [17]

Answer:

Hypotenuse would be 14

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Are the graphs 8x+3y=6 and 8x-3y=6 perpendicular

Alla [95]

Lines are perpendicular if the slope of one is the negative reciprocal of the other. In this case the slopes are -8/3 and 8/3, so while negative they are not reciprocal. So no, the two lines intersect but are not perpendicular.

4 0

3 years ago