For this assignment, you submit answers by question parts. The number of submiss

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For this assignment, you submit answers by question parts. The number of submissions rema Assignment Scoring Your best submission for each question part is used for your score. ining for each question part only changes if you sub 3. 0/2 points | Preious Answers LarCalcET6 4.3 020 Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using in terval notation.) In x increasing decreasing Subrit Answer. Save Progress Practice Another Version > Home My Assignments Extension Requesf

Explanation / Answer

f(x) = (lnx)/x1/4

f '(x) = [(1/x)x1/4 - (lnx)(1/4)x1/4-1]/(x1/4)2         since (u/v)' = [u'v - uv']/v2

==> f '(x) = [x-3/4 - (lnx)(1/4)x-3/4]/(x1/4)2

==> f '(x) = [x-3/4 - (lnx)(1/4)x-3/4]/x

==> f '(x) = [1- (lnx)(1/4)]/x1/2+3/4

==> f '(x) = [1- (lnx)/4]/x5/4

function is increasing ==> f '(x) > 0

==> [1- (lnx)/4]/x5/4 > 0

==> 1- (lnx)/4 > 0

==> lnx < 4

==> x < e4

x - cannot be negative and zero

hence function increases in (0 , e4)

function decreasing ==> f '(x) < 0

==> [1- (lnx)/4]/x5/4 < 0

==> 1- (lnx)/4 < 0

==> lnx > 4

==> x > e4

Hence interval of decrease = (e4 ,0)

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