Help Me find the Absolute Maximum Value

[cv2yanks13]

Where in Interval does it Reach Absolute Maximum Value

The volume V (in cubic centimeters) of 1 kg of water is very closely approximated by the function

v= 999.87 - (0.06426)T + (0.0085043) T^2 - (0.0000679)T^3

for temperatures ranging from 0 degrees Celsius to 30 degrees Celsius. At what temp on this interval does the volume reach its absolute maximum value?

I understand how to get the absolute max values from looking at the graph... but I need to show ALL algebraic and calculus work... I believe I need to find this by finding what the critical points are... I'm a little confused on how to find that (I'm uncertain if I have the correct answer)... can someone please assist me with this problem?? I truly need someone's help

What I need help with is factoring out this equation to find the critical points... I'm lost... please help me out... I need a good homework grade...

 

[BigGlenntheHeavy]

\(\displaystyle 0 \ \le \ T \ \le \ 30, \ look \ at \ your \ endpoints.\)

 

[cv2yanks13]

glen I don't want to be a bother... but can you explain further... I'm so lost here!

 

[BigGlenntheHeavy]

\(\displaystyle V(T) \ = \ 999.87-.06426T+.0085403T^{2}-.0000679T^3, \ 0 \ \le \ T \ \le \ 30\)

\(\displaystyle V'(T) \ = \ -.0002037T^2+.0170806T-.06426 \ = \ 0, \ T \ \dot= \ 4, \ only \ critical \ point.\)

\(\displaystyle V(0) \ = \ 999.87 \ cu. \ cm.\)

\(\displaystyle V(4) \ = \ 999.74 \ cu. \ cm.\)

\(\displaystyle V(30) \ \dot= \ 1003.79 \ cu. \ cm.\)

\(\displaystyle See \ graph\)

[attachment=0:1mdcrvvn]vwx.jpg[/attachment:1mdcrvvn]

\(\displaystyle Hence, \ max \ occurs \ at \ endpoint \ T \ = \ 30.\)

 

[cv2yanks13]

thanks man... god bless you.. that was a tough question... sometimes I just need someone to lay it out for me... explain... and then I get it...