Find the maximum and the minimum values of #f(x)=3x^4-8x^3+6x^2# on #[-1/2,1/2]# by finding the points where the derivative is 0 and compering with the values at the end point?

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Answer 1 · 2018-04-11T00:08:33

#f'(x)=0#

#0=3x^4-8x^3+6x^2#

#0=(x^2)(3x^2-8x+6)#

use the quadratic formula to find that #3x^2-8x+6# have factors .610 and -3.277

#x= 0, .610, -3.277#

since range is [-.5, .5], x=0

find max/min value, plug x=0 into f(x)

compare answer with f(-.5) and f(.5)

you should be able to do the rest youself