Find all the relative extrema of the function

Question

Find all the relative extreme of the function. If the answer does not exist use DNE.

y=ln(4x)-8x²

^{Relative minimum =}

^{Relative maximum =}

Answer 1

The domain interval of the function is (0,∞)

y' = 1/x-16x

1/x-16x = (1-16x²)/x = 0

x = ± 1/4 But -1/4 is not in the domain

y''(x) = -1/x²-16

y''(1/4) = -32 <0 Maximum by second derivative test

Relative Minimum DNE

Relative Maximum (1/4, -1/2)