need help (1 Viewer)

[bboyelement]

(i) differentiate with respect to x the function h(x) = (log₁₀x)/x

(ii) given the only stationary point is a maximum deduce without calculating any numerical values, e^pi > pi^e

i cant do the second part

 

[Riviet]

Solving h'(x)=0 yields x=e and given that this stat point is a maximum,

h(e) > h(pi)

(log₁₀e)/e > (log₁₀pi)/pi

Cross multiply and bring up the power:

log₁₀(e^pi) > log₁₀(pi^e)

Hence e^pi > pi^e

 

[zeek]

well if ur differentiating in the first part... im guessing that in the second part you might have to use the second derivative...

im trying to get something going based on the fact that its a stationary maximum .: h'(x)<0 and also h"(x)<0 .: h'(x)<h"(x) and then putting x=pi...

EDIT:

hahahaha or maybe not

 

[bboyelement]

ohh thanks ... i didnt think about that