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