Use the definition of derivative to find the slope of the tangent of f at x=-1. Then find an equation of the tangent line. f(x) =3x^2

Question

raden · Answer

m = f ' (1)
can u find the derivative of f, first ?

raden · Answer

oppp..
m = f ' (-1), i mean

anonymous · Answer

So do i just plug -1 in as x in f(x)=3x^2?

raden · Answer

that's used too, the other componet is f ' (-1)
so, find f ' first ?

anonymous · Answer

How do I find f ' ? this is in a math packet I have to do but we were never taught derivatives

anonymous · Answer

$$f'(-1)=\lim_{x\to -1}\frac{f(x)-f(-1)}{x+1}$$

anonymous · Answer

that is by the "definition"

anonymous · Answer

How do I use that to find the sloap of the tangent to f at x=-1? or it that it?

anonymous · Answer

$$\frac{3x^2-3}{x+1}=\frac{3(x+1)(x-1)}{x+1}=3(x-1)$$ then replace $x$ by $-1$ and get 
$$3(-1-1)=-6$$

anonymous · Answer

slope*

anonymous · Answer

that is the slope, $-6$

anonymous · Answer

and the equation of the tangent line?

anonymous · Answer

you have the slope, it is $-6$ and you have the point, it is $(-1,3)$ use the "point-slope" formula