Find the equation of the line tangent to the graph

Question

Find the equation of the line tangent to the graph of f(x)=(ln x)^3 at x=2

Answer 1

Want y=mx+b

f(x)= (ln(x))³

f'(x) = 3(ln(x))²/x

m=f'(2) = (3/2)(ln(x))²

At (2,f(2))

y-f(2) = m(x-2)=f'(2)(x-2)

f(2) = (ln(2))³

y = (3/2)(ln(2))²(x-2)+(ln(2))³

y = (3/2)(ln(2))²x-3(ln(2))²+(ln(2))³