Question

Find an equation of the tangent line to y = f(x) at x = a. Graph y = f(x) and the tangent line, to verify that you have the correct equation. f(x) = x^2 - 2, a = 1.

Answer 1

first find f'(x) at x=a

Answer 2

how do i do that?

Answer 3

it would be f'(a)=2a
line equation: f(x)-f(x_0)=b(x-x_0)
in this casen x_0=a, and b= 2a
So: f(x)-a^2+2=2a(x-a), or writing it other way: y-a^2+2=2a(x-a)
reoganizing a bit: y=2ax+(a^2-2-2a^2) , y=2ax-(a^2+2)

Answer 4

if a=1,
y=2x-3

Answer 5

ok

Answer 6

so how would i graph it?

Answer 7

ok the dot is at -3?