Find all relative extrema

[kegray0513]

Ok so I have a problem with finding the relative extrema. I know you can find the 2nd derietive and then make it equal to 0 but I can get to finding the 2nd derievtive and them I get confussed and lost.

The problem is..
f(t)=-0.0129t^4+0.3087t^3+2.1760t^2+62.8466t+506.2955

I have found f'(t) to be -0.0516t^3+0.9261t^2+4.352t+62.8466

and f''(t)=-0.1548t^2+1.8522t+4.352 and then I am lost!!! For this problem I also have to find the inflection points so I am not sure even where to start to find those if I need the diervitaves or not! Thanks for any help!

 

[BigGlenntheHeavy]

$\displaystyle f(x) \ = \ .0129t^{4}+.3087t^{3}+2.176t^{2}+62.8466t+506.2955$

$\displaystyle f'(x) \ = \ .0516t^{3}+.9261t^{2}+4.352t+62.8466, \ one \ critical \ point \ (-17.1674,-372.7069), \ Min.$

$\displaystyle f"(x) \ = \ .1548t^{2}+1.8522t+4.352, \ Pts. \ of \ Infx. \ (-3.21176,318.0307) \ and \ (-8.7533,-8.4046)$

$\displaystyle Note: \ Did \ this \ on \ my \ trusty \ TI-89.$

$\displaystyle See \ Graph.$

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