HOw do I find the equation of the tangent line?

Question

anonymous · Answer

This is the problem I'm working on.

anonymous · Answer

did you find the derivative

anonymous · Answer

i'm trying to use the f(x)-f(a) /(x-a) formula

anonymous · Answer

well since you have to find the derivitive in the first place its easier to just you it

anonymous · Answer

at first I thought it was 4x+3 but I don't think it is.

anonymous · Answer

f'=4x+3 is correct

anonymous · Answer

so this will give you the slope at any point of the graph

anonymous · Answer

yep i agree

anonymous · Answer

to find the slope at a specific point like a = 2, first plug in 2 for x in your f(x) equation to get the y value for the point

anonymous · Answer

a = -2 sorry

anonymous · Answer

that's it?

anonymous · Answer

no that will give you
f(-2) = -4. so that tells you that the point you want to find the slope at is (-2,-4)

anonymous · Answer

not -4 but -2
the point is (-2,-2)

anonymous · Answer

my bad again, im getting messed up. f(-2)=0. so the point is (-2, 0) that is finally right

anonymous · Answer

so your equation for the tangent line is 
y'=4x+3. plug in x = -2 to find the slope at that point

anonymous · Answer

okay, so I plug in -2 into f'(x) = 4(x) +3 I get -5 which is the slope.

anonymous · Answer

then I take that and put it in to slope formula y= mx +b?

anonymous · Answer

yes -5 is the slope at the point (-2,0)
so for the equation of a line
you need 
y=mx+b
your m you just found was -5

anonymous · Answer

use the -2 and 0 foe the x an y to find b

anonymous · Answer

so y = -5x-10

anonymous · Answer

yep

anonymous · Answer

I guess I'm just a little confused on how you got these points yes -5   (-2,0). a was given so that's my x and just set y to 0?

anonymous · Answer

y=4x+3
you get the slope of the tangent line by pluging in x=-2
remeber when i said to find f(-2). That gives you your y value for the point which was 0.
so in y=mx+b you have
y=(-5)x+b
the point you are looking at is the (-2,0) 
so you plug those into 
y=-5x+b and solve for b

anonymous · Answer

Oh i see now...  part b point (a, f(a)) .Awesome!

anonymous · Answer

no prob

anonymous · Answer

Thank you so much! Been so much help.

anonymous · Answer

your very welcome. sorry for the misscalculations at the first.