extrema, infl. pts. of y=x^4 log_(x). I get y'=x^4/xln3+...

[jtmaupin]

Greetings,

The problem I am working on has me a bit stumped. The question is find all relative extrema and points of inflection of y=x^4 log_3(x). I tried to approach the problem using the products rule but I ended up with y'=(x^4) * d/dx(log_3(x))+d/dx(x^4)*log_3(x). Which should yield y'=(x^4)*(1/xln3)+(4x^3)(logx/log3) => y'=x^4/xln3+4x^3(log(x)/2log(2)) after reducing y'=x^4/xln3+2x^3(log(x)/log(2)). My question then is am I done, or should I match the quotients which sounds messy.

 

[Deleted member 4993]

Re: Calc 1 help

The problem I am working on has me a bit stumped. The question is find all relative extrema and points of inflection of y=x^4 log_3(x). I tried to approach the problem using the products rule but I ended up with y'=(x^4) * d/dx(log_3(x))+d/dx(x^4)*log_3(x). Which should yield y'=(x^4)*(1/xln3)+(4x^3)(logx/log3) => y'=x^4/xln3+4x^3(log(x)/2log(2)) where did log(2) come from? after reducing y'=x^4/xln3+2x^3(log(x)/log(2)). I would convert in terms of ln(x) - because we need to find y" for point of inflection

 

[jtmaupin]

the 2log(2) might have been a typo. So how do I go about converting log to ln... its been awhile... can I just make them all ln?

 

[Deleted member 4993]

Looks like you really did not calculate the y' - somebody did it for you and that's why you have a typo.

Hint for conversion

\(\displaystyle log_a(x) \, = \,\frac{ln(x)}{ln(a)}\)