Need assistance with x intercepts and local extrema

[John45]

Im having trouble with my home work and can't seem to get the answers right

For this one I need to find the cordinates of the x intercept(s)

y=x*sqrt(10-x^2)

I think its (0,0) , (-sqrt(10),0), and (sqrt(10), 0) but i am not sure if the sqrt of 10 is in sismpliest form either

For this next one I need to know where local maxima occurs and local minima

y=x^(4/5)*((9/4)+x)

I thought it was 1 but it was incorrect

this next one I need to know were local maxima occurs, where local minimia occurs, and points of inflection that exist

y=4x+4*sqrt(2)*cos(x) on the interval [0,2Pi]

I thought maxima occured at (pi/4) but that was incorrect as well

 

[tkhunny]

Well, you had better figure out that \(\displaystyle \sqrt{10}\) is in simplest form. I'm tempted to put you back in algebra for not being sure of that. Are there any perfect square factors of 10?!

You thought what was "1"? Please show yoru work and use complete sentences. Your first task on this one is to determine if it exists for x < 0. Your graphing calculator probably will not get this right. You may need to rewrite your expression to get it to stop using logarithms to evaluate it for x < 0. After that, you may wish to investigate x = -1 for a local maximum - THEN there is the surprise. The derivative does nto exist at x = 0. You tell me what you shoudl do with that.

That's enough for now. Please PLEASE show some work. Make us believe you have SOME idea concerning what you are trying to do.