Question

equation of the tangent line to f(x)3x+1 at x=1

Answer 1

\(\large\color{black}{ \displaystyle f(x)=3x+1 }\)

Answer 2

Yes

Answer 3

interesting you are finding a tangent line to tangent line ?

Answer 4

so it would just be 3 correct

Answer 5

I will disappoint you that it will be this same line.

Answer 6

f`(x)=3

Answer 7

yes, but finding tangent line to a line is silly.

Answer 8

it is going to be this very same line 3x+1

Answer 9

maybe you have miss-written the function f(x) ?

Answer 10

this is what the whole problem says.
" Find the equation of the tangent line to f(x)=3x+1 when x=1"

Answer 11

I will show you the abstract side of it.

Answer 12

ohh see what yore saying i just graphed the line
its a tangent itself

Answer 13

tangent line to function \(\large\color{black}{ \displaystyle f(x)=mx+b }\) at \(\large\color{black}{ \displaystyle x=a }\)

\(\large\color{black}{ \displaystyle f'(x)=m }\)
\(\large\color{black}{ \displaystyle f'(a)=m }\)

point on the function when x=a, is also the same point on the tangent line.
\(\large\color{black}{ \displaystyle f(a)=ma+b }\)
point (a, ma+b)

\(\large\color{black}{ \displaystyle y-(ma+b)=m(x-a) }\)
\(\large\color{black}{ \displaystyle y=m(x-a)+(ma+b) }\)
\(\large\color{black}{ \displaystyle y=mx-ma+ma+b}\)
\(\large\color{black}{ \displaystyle y=mx+b}\)

Answer 14

congrants that same tangent line to any linear function at any x=a.

Answer 15

so the answer would be itself just to confirm

Answer 16

yes.

Answer 17

thanks for your help

Answer 18

for any curve f(x) if it is linear, and at any x=a.

Answer 19

yw

Answer 20

what would be the antiderivate of f(x)=-x^2+2

Answer 21

integrate it.

Answer 22

\(\large\color{slate}{\displaystyle\int\limits_{~}^{~}x^n~dx=\frac{x^{n+1}}{n+1}}\) (roughly)

Answer 23

and
\(\large\color{slate}{\displaystyle\int\limits_{~}^{~}ax^n~dx=\frac{ax^{n+1}}{n+1}}\)

Answer 24

oh thats a lot
I'm asking because they're asking me to graph f(x) but they gave me f'(x)
the equation of f '(x) is -x^2+2

Answer 25

i just figured it would be a tad more simpler than integration