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solniwko [45]
2 years ago
7

The equation of a curve is y = x³ + 4x. Show that the value of y increases when x increases. ² is a decreasing function.​

Mathematics
1 answer:
belka [17]2 years ago
7 0

We will see that f'(x) > 0, which means that f(x) is an increasing function.

<h3>How to prove that the function is increasing?</h3>

For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.

Here we have the cubic function:

f(x) = x³ + 4x

If we differentiate this, we get:

f'(x) = df(x)/dx = 3x² + 4.

And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.

If you want to learn more about cubic functions:

brainly.com/question/20896994

#SPJ1

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Franks bookshelf is 1 1/2 meters high. Each row in the bookshelf is 3/16 of a meter high. How many rows are there in franks book
levacccp [35]

Answer:

29 rows.

Step-by-step explanation:

  1. Turn 11/2 and 3/16 into a fraction
  2. 11/2 = 5.5 and 3/16 = 0.1875
  3. Divide 5.5 by 0.1875 = 29.3333333333
  4. Round up and get 29 since .3333333333 does not equal a whole shelf.
7 0
4 years ago
The location x of a car in meters is given by the function x = 30t - 5t^2 where t is in seconds. At the time when the car is mov
EastWind [94]

So, how far is the car from where it was at t = 0 is 40 m

<h3>Velocity of the car</h3>

Since the location x of the car in meters is given by the function x = 30t - 5t² where t is in seconds, we need to find the time at which its velocity is 10 m/s in the negative direction by differentiating x with respect to t to find its velocity, v.

So, v = dx/dt

= d(30t - 5t²)/dt

= d30t/dt - d5t²/dt

= 30 - 10t

When v is 10 m/s in the negative direction, v = -10 m/s.

So, v = 30 - 10t

-10 = 30 - 10t

-10 - 30 = -10t

-40 = -10t

t = -40/-10

t = 4 s

<h3>The distance at 4 s when its velocity is -10 m/s</h3>

Since at t = 4 s, its velocity is -10 m/s and x = 30t - 5t² is the car's location. The car's distance from t = 0 after its velocity is -10 m/s is

x(4) - x(0) = 30(4) - 5(4)² - [30(0) - 5(0)²]

= 120 - 5(16) - [0 - 0]

= 120 - 80 - 0

= 40 m

So, how far is the car from where it was at t = 0 is 40 m

Learn more about distance of car here:

brainly.com/question/17097458

6 0
3 years ago
I know how to convert degrees into degrees-minutes-seconds. I was just wondering about the negative and 0°. The original degree
ratelena [41]
I think the answer will be like
0degree 55minutes 21seconds
That in the negative side
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3 years ago
What is the measure of angle ABD in trapezoid ABCD?<br><br> 24°<br> 40°<br> 64°<br> 92°
tangare [24]
The answer is 24!!!!!!
3 0
3 years ago
Sandy is 6 inches taller than Marie. If Marie
Zarrin [17]
If Marie is 5 inches that Would make sandy 11 inches. So for every odd inch that Marie may be add 6 inches to represent Sandy”s height. I hope this somewhat helps or gives you an idea of what to do
5 0
4 years ago
Read 2 more answers
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