Estimate the slope of the tangent line at the point x=3; f(x)=lnx

Answer 1

“Estimate the slip of a tangent line” is a fancy way of saying “take the derivative.” Thinking of derivates as the slope of a curve at a given point is in my opinion the easiest way to visualize otherwise complicated calculus.

The derivate of ln(x), with respect to x, is always 1/x. This is one of the useful identities to commit to memory.

Now that we know f’(x) = 1/x, we can solve that function at x=3.

f’(3) = 1/3