differentiaton applications help

lavastar SG

1) The equation of a curve is given by lg X / X, x>0. Given that the only stationary point of the curve is a maximum, deduce without calculating any numerical values, that e^pi > pi^e

Note: pi = the symbol which has a value of 3.14. e^pi means e to the power of pi and same for the another.

2) Given that x increases at the rate of 2 units per second, find in terms of A the rate of change of ln(xy) when y = 4A. [Ans: 11/12 A]

Thanks for those who can help

unclebutcher SG

i in school now see if i can help when i reach home

eagle SG

Are you A levels? If so, you should be able to differentiate lg X.

in any case, after differentiating, you set it to zero
you will solve x = e as the maximum pt

thus,
lg e / e is the max value of the curve. Any other value is smaller.

lg e / e > lg pi / pi
pi * lg e > e * lg pi
lg e^pi > lg pi^e

Thus, we get e^pi > pi^e (solved)

any other relation between x and y?