f(x)= 2x^4 - 16x^2 +3; on 0,2
I got to 8x^3 -32x=0 what do I do now?
Use the maximum-minimum principle:
calculate a value c in the interval [0,2] such that f'(0)=c or doesnt exist
list endpoints of interval: 0,c1,c2,c3....,2
express f(x) for each value of c above
The largest is absolute maximum and the smallest is absolute minimum
OR you could just differentiate again OR just draw a graph to check your answer. Have you got mathcad or a similar graphing programme? There are online sites that calculate the graph based on an inputted function (but dont know if I can mention here - just google)
Set f'(x)=0 and solve for x. That will give you the x value(s) where your local max/min occurs.
But since f(x) is on an closed interval (I believe you meant to write [0,2]?), you also need to check the endpoints too.