# Thread: Line tangent to f(x)

1. ## Line tangent to f(x)

I'm not into this topic yet but wanted to get ahead.

Find the equation of line tangent at point (1,5):

$
f(x)=2x^2+3x^3
$

so will this be something like:

$
4x+9x^2
$

I forgot how to do this type I know it has something to do with y = mx + b

2. Originally Posted by drkidd22
I'm not into this topic yet but wanted to get ahead.

Find the equation of line tangent at point (1,5):

$
f(x)=2x^2+3x^3
$

so will this be something like:

$
4x+9x^2
$

I forgot how to do this type I know it has something to do with y = mx + b
Yes, the slope of the tangent line at any point on the graph is

$f'(x)=4x+9x^2$

So, when x=1, the slope of a line tangent to $f$ is $f'(1)=13$

Therefore the equation to that line is

$(y-5)=13(x-1)$ in point slope form. You can rewrite to obtain the y-intercept form.

3. $

4x+9x^2
$
There is a SUPER easy reason why this is not the equation of the tangent LINE. It is something important though.

You are on the right track though. However, this is one of the problems with using rules of derivatives without knowing fully why we are using them.

If we are interested in finding the equation of the line tangent to the point $(x,f(x))$, then we need to find some informatinon, most importantly what is the SLOPE of the line tangent to that point. But the slope of that line (if it containts that particular point), will be the same slope of that CURVE at the point $(x,f(x))$ yes?

Do you know what this $
4x+9x^2
$
actually refers to?

4. well it might not be the equation of the line, but that's just how I started.

This is how I finished it. Like VonNemo19 said.

5. Originally Posted by drkidd22
well it might not be the equation of the line, but that's just how I started.

This is how I finished it. Like VonNemo19 said.

Everthing is correct except for your last stement in the left column.

IE. $m=13$, not $(1,13)$. This is a technical thing. But in essence, you have done well

6. Don't worry, I wasn't trying to bust you out - just hoping to correct a misunderstanding before it becomes engrained as fact for you.

7. Originally Posted by drkidd22
well it might not be the equation of the line, but that's just how I started.

This is how I finished it. Like VonNemo19 said.
I think ANDS' point was that it is very hard to understand what you are saying if you don't say what you mean!

What you said was
"Find the equation of line tangent at point (1,5):

$f(x)= 2x^2+ 3x^3$

so will this be something like:
$4x+ 9x^2$"