A critical point is an interior point of the domain of a function where the derivative is zero or undefined.
Since f(x) is a polynomial, all points of f(x) and f'(x) are defined over ℝ.
Thus it is essential to find all points where f'(x)=0,
4x³-12x²+8x=0
which factors easily to:
4x(x²-3x+2)=0
Can you take it from here?
find all critical points of f(x) = x^4 – 4x^3 + 4x^2
1 answer
1 answer