1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ganezh [65]
3 years ago
14

How to determine open interval on which the function is increasing?

Mathematics
1 answer:
emmasim [6.3K]3 years ago
7 0

Answer:

To find when a function is increasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing.

You might be interested in
Dolores is going to make a sandwich. She has 2 types of bread, 3 types of cheese, and 2 types of meat to choose from. How many d
loris [4]
Twelve hours later then we went to sleep and then woke me back at my house after my birthday and I got invited
5 0
2 years ago
Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)
babunello [35]

\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k

We want to find f(x,y,z) such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=x^2+y

\dfrac{\partial f}{\partial y}=y^2+x

\dfrac{\partial f}{\partial z}=ze^z

Integrating both sides of the latter equation with respect to z tells us

f(x,y,z)=e^z(z-1)+g(x,y)

and differentiating with respect to x gives

x^2+y=\dfrac{\partial g}{\partial x}

Integrating both sides with respect to x gives

g(x,y)=\dfrac{x^3}3+xy+h(y)

Then

f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)

and differentiating both sides with respect to y gives

y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C

So the scalar potential function is

\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}

By the fundamental theorem of calculus, the work done by \vec F along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it L) in part (a) is

\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}

and \vec F does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them L_1 and L_2) of the given path. Using the fundamental theorem makes this trivial:

\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3

\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4

8 0
3 years ago
Graph of f(x) = 100(0.7)x
Lana71 [14]

Answer:

pay attention in class :)

Step-by-step explanation:

7 0
3 years ago
Can anyone please help me with these questions please. thanks.
Pani-rosa [81]
1.) 3/4
2.) It snowed 1/4 more on Tuesday than it did on Monday.
3 0
3 years ago
Read 2 more answers
The volume of this rectangle prism=____ft3.
serious [3.7K]

Answer:

18

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • A square pyramid has a height h and a base with side length b. The side lengths of the base increase by 50%. Write a simplified
    13·1 answer
  • Tristan walked for 13 1/4 hours in May and June altogether. In May, he walked 6 4/6 hours. How many hours did he walk in June?
    15·1 answer
  • in a box of 360 building blocks, 3 out of every 8 are green. which of the following is the number of green building blocks in th
    12·2 answers
  • Can a parallelogram have two 45 degree angles and two 75 degree angles? Why or why not?
    11·2 answers
  • a company has decreased the weight of its boxes of macaroni by 8 %. if the new weight of the box is 15.1 ​ounces, what was the o
    8·2 answers
  • in order to encourage students to show up early to a school dance , the dance comittee decides to charge less for those who come
    12·1 answer
  • Hello peoples help answer this? :>
    14·2 answers
  • Without doing any calculations, determine the missing number that will make the value of Expression B half the value of Expressi
    9·1 answer
  • Write an Inequality statement that is represented by the following graph
    14·1 answer
  • ✺༒Question༒✺<br><br>Refer to attachment <br><br>Nonsence answer will get report​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!