Find the tangent line equation to the curve y = f(x) = ln(6x^6) at x = (e/6 )^1/6 .

Question

Essentially getting it to Y-Y1=m(X-X1) form and solving it is where I'm having trouble.

Answer 1

Using log properties, ln(6x⁶) = ln6 + ln(x⁶) = ln6 + 6lnx

So, the derivative is 6/x

Also, when x = (e/6)^1/6, y = ln6 + 6ln(e/6)^1/6 = ln6 + ln(e/6) = ln6 + lne - ln6 = 1

Now, use the point-slope form.

Answer 2

Devin,

to find "m," you take the derivative and evaluate the given "x"

to find Y1, you evaluate the given "x" in the function

X1 is given

Can you say where you are having trouble?

Andrew F.