SOLUTION: Find an equation of the tangent line at the point indicated. f (x) = log6 (5x + x^-5), x = 1

Question 418868: Find an equation of the tangent line at the point indicated.
f (x) = log6 (5x + x^-5), x = 1
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First let's find the y-coordinate of "the point indicated":

f(1) = 1
So "the point indicated" is (1, 1)

Now we find the slope of the tangent at this point. For this we will need the first derivative Using the dervative of a logarithm plus the chain rule we get:
f'(x) =
To find the slope at (1, 1) we need
f'(1) =
which simplifies as follows:
f'(1) =
f'(1) =
f'(1) = 0

A line, with a slope of 1, though the point (1, 1) would be y = 1. This is the equation for the tangent line.

Here's a graph of f(x):

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