f(x) = 8x - 3 ln(x), x > 0. List all critical numbers of f . If there are no cri

Question

f(x) = 8x - 3 ln(x), x > 0. List all critical numbers of f . If there are no critical numbers, enter 'NONE'. Critical numbers = Use interval notation to indicate where f (x ) is increasing. Note: Use INF for infinitive, '-INF for - infinitive. and use 'U' for the union symbol. Increasing: Use interval notation to indicate where f ( x ) is decreasing. Decreasing: List the x-coordinates of all local maxima of f . If there are no local maxima, enter 'NONE'. x values of local maxima = 0 List the x-coordinates of all local minima of f . If there are no local minima, enter 'NONE'. x values of local minima =

Explanation / Answer

f(x)=8*x-3*ln(x) f'(x)=8-(3/x) f'(x)=0 8=3/x x=3/8 so critical point is (3/8,3-3*ln(3/8)) b) for increasing f'(x)>0 so interval=(3/8,inf) C) decreasing interval=(-inf,3/8) D)NONE E)3/8

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