find value of k

Question

find all values of k such that f(x)=x^3+2x^2+kx+1 is one-to-one

(knowing this question is related to the inverse functions)

Answer 1

Derivative f'(x) = 3x^2 + 4x + k is quadratic function must be nonnegative for all x, then f(x) is increasing function and one-to-one. Discriminant 16 -12k <= 0 0, k >= 4/3. For k >= 4/3 f(x) is one-to-one function