Use the derivative of the function y=f(x) to find the points at which f has a local maximum, local minimum or point of inflection.
y ' = 6(x+1)(x-2)^2
help me with this problem, thank you
You already know that *
At an extremum,
That is .
To know the nature of these points we compute the second order derivative.
If x = -1 then and we have a minimum.
If x = 2 then and we have a point of inflection.
We also have a point of inflection at x=0 because .