Question

F (x)=x4-3x3+3x2-x local maximum or minimum

Answer 1

Answer:

x=1 is point of inflection and x=1/4 is point of local minima.

Explanation:

F(x) = x^4 - 3x^3 + 3x^2 - x

F'(x) = dF(x)/dx = 4x^3 - 9x^2 + 6x - 1

F'(x) = 0

(x-1)^2 × (4x-1) =0

F''(x) = d^2F(x)/dx^2 = 12x^2 - 18x + 6

Now, it can be seen that on x = 1, F''(x) = 0.

It means x = 1 is point of inflection (where tangent intersects the curve).

And at x = 1/4, F"(x) = 2.25 > 0

So x = 1/4 is a point of local minima.

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