What is the maximum value of y = 3x^2 - ln x + 1 if it has one.

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justaguide eNotes educator| Certified Educator

The function y = 3x^2 - ln x + 1. The maximum value of the function lies at x = a if x = a is the solution of y' = 0 and y'' is negative for x = a.

y = 3x^2 - ln x + 1

y' = `(6*x^2-1)/x`

y'' = `(6*x^2+1)/x^2`

As x^2 is always positive, the value of y'' is positive for all values of x.

The graph of the given function is:

The given function y = 3x^2 - ln x + 1 does not have a maximum value.