What are the local maxima and minima of #f(x) = 4x^3 + 3x^2 - 6x + 1#?

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Answer 1 · 2015-11-12T16:27:30

Polynomials are differentiable everywhere , so look for the critical values by simply finding the solutions to #f'=0#

#f'=12x^2+6x-6=0#

Using algebra to solve this simple quadratic equation:

#x=-1# and #x=1/2#

Determine if these are min or max by plugging into the second derivative:

#f'' = 24x+6#

#f''(-1) <0#, so -1 is a maximum

#f''(1/2)>0#, so 1/2 is a minimum

hope that helped

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