How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for #f(x) = 2x + ln x#?
This function increases on the interval: (-infinity,-1/2)u(0,infinity) and decreases on the interval: (
To figure this out we must first take the derivative of the function which is
Secondly, the derivative is negative from the x-intercept to 0. So the function decreases from
Relative maxima occur at x-intercepts of the derivative where it goes from positive to negative (because this is where the function goes from increasing to decreasing) and this only occurs at
Relative minima occur at x-intercepts of the derivative where it goes from negative to positive (because this is where the function goes from decreasing to increasing). This never occurs due to the vertical asymptote so there are no relative minima for this function. Hope I helped! Sorry if this was confusing, I was a little rushed!