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3 years ago

Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?

1 answer:

4 0

The derivative is the rate of change of a function, basically represents the slope at different points. To find the derivative of the given function you can use the power rule, which means, if n is a real number, d/dx(x^n)= nx^(n-1). This is a simplification of the chain rule based on the fact that d/dx(x)=1. Anyway, this means that d/dx(x^3 + 1)= 3x^2. Here n is 3 and so it is 3*x^(3-1)= 3x^2. The derivative of x^3+1 is 3x^2.

If you are wondering what happened to the 1, for any constant C, d/dx(C)=0.

You might be interested in

Which equation could be used to find the height of the flagpole

Sauron [17]

X = height of pole (in meters)

With respect to the 50 degree angle, the side x is the opposite leg. It is the leg furthest from the reference angle. The hypotenuse is 5 meters.

The trig function sine ties together the opposite and hypotenuse

sin(angle) = opposite/hypotenuse
sin(50) = x/5
5*sin(50) = x .... multiply both sides by 5
x = 5*sin(50)

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Since x = 5*sin(50) isn't listed as an answer choice, let's try using cosine. We can't use it right away because we don't know the adjacent side. What we can do is change the reference angle. The missing angle of the triangle is 90-50 = 40 degrees. Let's make the 40 degree angle the reference angle

So x is now the adjacent side with respect to the 40 degree reference angle. The hypotenuse is always the longest side. The hypotenuse stays at 5.

cos(angle) = adjacent/hypotenuse
cos(40) = x/5
5*cos(40) = x
x = 5*cos(40)

This expression is listed. The answer is choice B

4 0

3 years ago

Can anyone answer me pls I need help

Afina-wow [57]

Answer:

4,9

Step-by-step explanation:

i looked it up on a website,uhhhhh i don't know if its completely write soooo.....

8 0

3 years ago

Read 2 more answers

What is the greatest decimal in hundredths that can be rounded to 14.5? What is the least

olga55 [171]

Answer:

14.45 and 14.54

Step-by-step explanation:

Rule for rounding:

Round up if number is between 5 and 9
Round down if number is between 0 and 4

What numbers in hundredths can be rounded to 14.5?

14.45 to 14.49

and

14.50 to 14.54

From above we see that:

The greatest decimal is 14.54
The least decimal is 14.45

7 0

3 years ago

Zachary purchased a computer for 1800 on a payment plan. Three months after he purchased the computer, his balance was 1350. Fiv

zubka84 [21]

Solution-

Zachary purchased a computer for 1800 on a payment plan. (Initial Money)

3 months after he bought the computer, his balance was 1350. (Money after 3 months)

Total money paid in 3 months = 1800-1350 = 450

Money paid per month = 450/3 = 150

5 months after he bought the computer, his balance was 1050.

Total spent = 1800-1050 = 750 = (5× 150)

So the equation that models the balance b after m months,

b = 1800 - m(150)

∴ Here, the slope signifies the constant monthly deduction of $150.

3 0

3 years ago

A jet plane can carry up to 200,000 liters of fuel. It used to 130,000 liters of fuel during a flights. What percentage of the f

LekaFEV [45]

65%
Step-by-step explanation:
Given: Full capacity= 200000 litres
Amount of fuel used during flight= 130000 litres
Now, finding percentage of fuel used on the flight.
∴ Percentage of fuel used=
Solving it, we will get
∴ 65% of fuel capacity been used in this flight.

7 0

3 years ago