All categories

3 years ago

What are the coordinates of the turning point for the function f(x) = (x+3)^3 + 1

Mathematics

2 answers:

Charra [1.4K]3 years ago

5 0

Answer:

The turning points for the given function is (-3,1).

Step-by-step explanation:

The given function is

$f(x)=(x+3)^3+1$

The turning point of a function where the $f'(x)=0$ .

$f'(x)=3(x+3)^2$

Equate the first derivative equals to 0.

$0=3(x+3)^2$

$x+3=0$

$x=-3$

At the turning point the x-coordinate is -3.

Substitute x=-3 in the given function.

$f(-3)=(-3+3)^3+1$

$f(-3)=1$

At the turning point the y-coordinate is 1.

Therefore the turning point is (-3,1).

andrey2020 [161]3 years ago

4 0

The turning point is just the minimum/maximum so the coordinates are (-3,1) which you find from the expression of (x+3)³ + 1

You might be interested in

Online jewelry sales have increased steadily over the last 10 years. In 2003, sales were approximately 2 billion dollars, and in

UNO [17]

Answer:

$rate\ of\ increase = 28.8\ billion\ dollars\ per\ year$

model: $y = 28.8(t-2003) + 2$

profit in year 2017: $y = 405.2\ billion\ dollars$

Step-by-step explanation:

The sales increased from 2 billion dollars to 146 billion dollars in five years, so to find the increase in billion dollars per year, we just need to divide the increase by the amount of time:

$rate\ of\ increase = (146 - 2)/5 = 144 / 5 = 28.8\ billion\ dollars\ per\ year$

To construct a model for these sales, we can use the year 2003 as the initial point of a linear equation:

$y = ax + b$

the variable y will represent the profit in billion dollars, the variable x will represent our time, so we can use (t - 2003) in its place to represent the number of years since 2003 (t is the year we want to calculate), the constant 'a' will be our rate of 28.8, and the constant 'b' is the inicial value for the year 2003, that is, 2 (billions). So we have:

$y = 28.8(t-2003) + 2$

In the year 2017, we would have:

$y = 28.8(2017-2003) + 2$

$y = 28.8*14 + 2$

$y = 405.2\ billion\ dollars$

6 0

3 years ago

For what values of x and y must the figure have in order to be parallelogram?

Oduvanchick [21]

Answer:

y = 10°

x = 64°

Step-by-step explanation:

Parallelogram is a quadrilateral with the opposite sides parallel to each other. Opposite sides are equal in length. Opposite angles are equal in a parallelogram.

For the figure to be a parallelograms, since opposite angle are equal

12y + 8 = 2x

2x - 12y = 8 ...................(i)

2x + 5y + 2 = 180(supplementary angle)

2x + 5y = 178..............(ii)

combine the equation

2x - 12y = 8 ...................(i)

2x + 5y = 178..............(ii)

make x subject of the formula in equation (i)

2x - 12y = 8 ...................(i)

2x = 8 + 12y

x = 4 + 6y

put the value of x in equation (ii)

2x + 5y = 178..............(ii)

2(4 + 6y) + 5y = 178

8 + 12y + 5y = 178

8 + 17y = 178

17y = 170

divide both sides by 17

y = 170/17

y = 10°

Put the value of y in equation (i)

2x - 12y = 8 ...................(i)

2x - 12(10) = 8

2x - 120 = 8

2x = 128

x = 128/2

x = 64°

7 0

3 years ago

Is there another way to write JK? Why or why not?

daser333 [38]

Answer:

What do u mean

. I'm confused

4 0

3 years ago

Read 2 more answers

Using a straightedge draw a random triangle now carefully cut it out next amputate the angles by snipping through adjacents side

Nezavi [6.7K]

This is usually used as a proof that triangles have 180°. Look at the attached figures. If you cut off angle A, angle B and angle C and rotate them so that their vertices touch, you form a half-circle out of them (or a straight line). We know that half a circle is 1/2 of 360° or 180; therefore all 3 angles in a triangle must add up to 180°.

4 0

3 years ago

9. Sonia bought 5 shirts that cost $38.00 each. If the tax rate is 8.5%, how much did Sonia pay?

qaws [65]

The answer is A

8.5% sales tax + 38.00= $41.23 x 5 (shirts)= $206.15

8 0

3 years ago