For y = 3x^4 - 2x^3 + x^2 + ax - b, what values of a and b give extreme points.

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The extreme points of a function f(x) are those where x is the solution of f'(x) = 0.

Here y = 3x^4 - 2x^3 + x^2 + ax - b

y' = 12x^3 - 6x^2 + 2x + a

The solution of 12x^3 - 6x^2 + 2x + a =...

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The extreme points of a function f(x) are those where x is the solution of f'(x) = 0.

Here y = 3x^4 - 2x^3 + x^2 + ax - b

y' = 12x^3 - 6x^2 + 2x + a

The solution of 12x^3 - 6x^2 + 2x + a = 0 depends only on the value of a. The value of b is not involved in the equation.

The roots of the equation have at least one real solution irrespective of the value of a. It can have a maximum of 3 real solutions.

For y = 3x^4 - 2x^3 + x^2 + ax - b to have an extreme point, a and b can take on any value.

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