Question

I would appreciate any help with this problem

"Find the equation of the tangent line to the graph of f at the given point: f(t) = (t-4)(t^2-6), at (2,4)

Answer 1

I think I start this problem by doing the product rule, but I'm not to sure

Answer 2

yes, to find the tangent at a point you will need the derivative at that point, so find f'(t)
and yes, it will require the product rule

Answer 3

Once I finish doing the product rule, would I just plug in the point ?

Answer 4

Couldn't that expression be simplified into a single polynomial?

Answer 5

"would I just plug in the point ?"
- Yes, but only the t=2 part; you can ignore the f(2)=4 for now.

Answer 6

Okay and when I find that answer would I be finished ?

Answer 7

or do I plug that into y=mx+b?

Answer 8

Not quite. That will get you the slope of the line, but you still need an equation for the line.

Answer 9

Yes, you'll have the slope and a point, so you can either use y=mx+b or y-y1=m(x-x1)

Answer 10

So I used y=mx+b and I got a final answer of y=-10x+24. Would you mind checking my answer ?

Answer 11

Alright, let me get my pencil . . .

Answer 12

Thank you

Answer 13

Ok, slope is correct...

Answer 14

Yes, that is the tangent line at that point. Good job!

Answer 15

Did you use the product rule?

Answer 16

woohoo! thank you very much for your help (:

Answer 17

In most cases when you have a product, product rule is the way to go, but this one easily simplified to t^3 -4t^2 -6t +24, so you could also differentiate term by term.