For the function f(x)=(x+3)^2 , find the equation of the tangent line to the graph of f at x=0. If the equation of the tangent line is written as y=mx+b, what are m and b ?

Answer 1

f(x) = (x+3)²

f(0) = 9

f'(x)= 2(x+3)

f'(0)=6=m

Tangent line at (0,9)

y-y₁ = m(x-x₁)

y-9=6(x-0)

y=6x+9

m=6

b=9