Question 7: Given the function y = f(x) = -x3 + (2m – 1)x2 – (2 – m)x – 2. Find m so that the graph of the function has a maximum and a minimum?

y = – x^{3 }+ (2m – 1)x^{2} – (2 – m)x – 2

TXĐ: D = CHEAP

y’ = – 3x^{2} + 2(2m – 1) – 2 + m

Graph of a function with a maximum and a minimum ⇔ Pt y’ = 0 has two distinct solutions

Δ’ = (2m – 1)^{2} + 3(- 2 + m) > 0 ⇔ 4m^{2} – m – 5 > 0 ⇔ m ∈ (-∞; -1) ∪ (5/4; +∞)

===============