How do you find the slope of a tangent line to the graph of the function # f(x) = 1/sqrt(6x)# at x=9?

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Answer 1 · 2017-03-20T11:50:45

Start by finding the derivative.

#f(x) =1/sqrt(6x) = 1/(6x)^(1/2) = (6x)^(-1/2)#

Now by the chain rule, letting #y = u^(-1/2)# and #u = 6x#, we have.

#f'(x) =-1/2u^(-3/2) * 6 = -3u^(-3/2) = -3/(6x)^(3/2)#

The slope of the tangent at #x =9# is

#f'(9) = -3/(6(9))^(3/2) = -3/54^(3/2)#

Hopefully this helps!