Question

How do you find the equation of the line tangent to the graph of `f(x)= (ln x)^5` at x=5?

Answer 1

`f ' (x) = 5 (ln x ) (1/x)`
`f ' (5) = 5 (ln 5) (1/5) = ln 5` ---- this is the slope
`f(5) = (ln 5 )^5`

`y-(ln 5)^5 = ln 5 (x - 5)`

Explanation:

Use chain rule to find derivative of f(x) and then put in 5 for x. Find the y-coordinate by putting in 5 for x in the original function then use the slope and the point to write the equation of a tangent line.