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**Unformatted text preview: **The derivative will equal 0 when the numerator equals 0 and the denominator does not equal 0. Write in exponential form. To determine whether the function has a relative maximum at x = 1, lets use the second derivative. This is the first derivative. Differentiate. " " f x ( ) = # x 2 $ 1 x # ln x $ # 2 x ( ) # x 2 ( ) 2 Simplify. Factor and cancel. Evaluate the second derivative at x = 1. Since the value of the second derivative is negative at x = 1, the function is concave down at x = 1. Therefore, the function does indeed have a relative maximum at x = 1. To find the y-coordinate of this point So, the relative maximum occurs at (1, 1)....

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