Question

I need to find the tangent line of f(x)=e^(3x)
any help is greatly appreciated

Answer 1

I know I need to take the derivative

Answer 2

so the derivative of
e^(ax)
is
ae^(ax)

Answer 3

\[f '=3e^{3x}\]

Answer 4

correct

Answer 5

yes and then I sub it into y-y1=m(x-x1)
sorry I should use subscripts

Answer 6

yes you evaluate the derivative at the requested point and it gives you the slope m

Answer 7

then you use the coordinates of the point as x1 and y1

Answer 8

that is where I am messing up

Answer 9

\[y-y_{1}=m(x _{1}-x)\]

Answer 10

no,
y-y1=m(x-x1)

Answer 11

\[y-1=3e^{3x}(x-0)\]

Answer 12

"you evaluate the derivative at the requested point and it gives you the slope m"

you need to plug into the derivative in your case x=0
and then plug it as m.

Answer 13

m = f'(x1)

Answer 14

so m=3

Answer 15

now I use the slope intercept correct? it has been a long time since I have seen this.....

Answer 16

ok got it y=3x+1 you are a lifesaver.....

Answer 17

good !

Answer 18

Thank you