Find the relative maxima and relative minima, and sketch the graph with a graphing calculator to check your results. (If an answer does not exist, enter DNE.)

Question

Find the relative maxima and relative minima, and sketch the graph with a graphing calculator to check your results. (If an answer does not exist, enter DNE.)

y = 5x ln(x)

relative maximum	(x, y) =		DNE
relative minimum	(x, y) =

Answer 1

Hello,

That's enough you find y' and y"

y = 5x ln(x)

y' = 5 Lnx + 5x* 1/x = 5Lnx +5 = 0 Lnx = -1 x = 1/e by replacing to the function we have

y = 5(1/e ) Ln(1/e) = -5/e so the point is A ( 1/e , -5/e )

y" = (5Lnx +5)' = 5/x by replacing point A y" = 5e >0 so this point A represents to the minimum

I hope it is useful,

Minoo