Tangent lines

Dec 2015
8
0
canada
Hello,

Determine the equations of the tangent lines to the graph of
f(x)=3x(5x^2+1)
that are parallel to the line
y=8x+9
This is what I have so far:
d/dx(3x(5x^2+1))=45x^2+3
45x^2+3=8
x=-1/3, x=1/3
When I sub this into my formula I get f=-14/9 and f=14/9. does this seem right?
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey bbbbbb.

Yes - that is correct for getting the value of x that matches the gradient but now you need to get the y-intercept.

Have you covered this before?
 
Dec 2015
8
0
canada
Hello Chiro,

How would I get the y-intercept?

No I haven't covered this before.
 
Dec 2015
8
0
canada
I am getting f=14/9 and f= -14/9 when I sub them into my original function.
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
remember the point-slope equation for a line?

$y=mx+b$ ... what does $b$ represent?

you know $y$, $x$, and $m$ ...
 
Dec 2015
8
0
canada
so, 8(1/3)+9=35/3 y=35/3
and,
8(-1/3)+9=19/3 y=19/3
Is this right?
 

Plato

MHF Helper
Aug 2006
22,489
8,652
so, 8(1/3)+9=35/3 y=35/3
and,
8(-1/3)+9=19/3 y=19/3
Is this right?
@bbbbbb, do you have a clue about any of this?
Looking at what you were given in replies #2 & #5 and then your response, it appears not.

How can we help if you are lost in the very basics?