Question

find all possible functions of f with the given derivative

Answer 1

@.Sam.

Answer 2

take the integral of it

Answer 3

hold on we r not yet there

Answer 4

\[\int\limits_{}^{}x dx=\frac{ x ^{2} }{ 2 }\]

Answer 5

ok lets think about it another way then.

Answer 6

For a derivative you take the power and bring it in front then take one off the power. Right??!

Answer 7

yes

Answer 8

Let's work backwards. We know the new power is 1 to what was the original?

Answer 9

so what**

Answer 10

2

Answer 11

i got it divide by 2 to cancel out 2

Answer 12

right?

Answer 13

Great, we also know that that 2 had to have been brought in front, but is now gone. So what would make that happen?...... Nice job. Want me to teach you integration. It's just as easy

Answer 14

yup plz and thanks

Answer 15

This is an integral sign \[\int\limits_{}^{}\]
The function is written like \[\int\limits_{}^{}f'(x)dx\]Where f'(x) is the derivative and that is why dx is behind it.
\[\int\limits_{}^{}x ^{n}dx=\frac{ x ^{n+1} }{ n+1 }\],

Answer 16

so that the formula right i would use that to find any function

Answer 17

integration is how you go from the slope back to the original equation

Answer 18

any function in that form. it does not work for x^-1. the integral of that is ln x. But for any other x^n it applies

Answer 19

where n is a constant

Answer 20

thx i got it

Answer 21

also should i need to put +c constant for every anti derivative

Answer 22

Ya you need to do it, I left that off to not overcomplicate my description, but yes if the integral is not defined you have to do it.

Answer 23

how to do with integrals if it quotient one like

Answer 24

\[\frac{ -1 }{ x^2 }\]

Answer 25

that is x^2