Question

Tìm y_Max , y_min (nếu có) của hàm số sau:

a, y = x⁴ + 3x² +2 trên [-2;3]

b, y = -x⁴ + 2x² +3 trên [-2;1]

c, y = (x² +x)(x+2)(x+3)

Answer 1

a: \(x\in\left[-2;3\right]\)

nên \(\left\{{}\begin{matrix}x^4\in\left[0;81\right]\\x^2\in\left[0;9\right]\end{matrix}\right.\Leftrightarrow x^4+3x^2\in\left[0;108\right]\)

=>\(y\in\left[2;110\right]\)

y=2 khi x=0

y=110 khi \(x^4+3x^2=108\)

=>x^4+12x^2-9x^2-108=0

=>x=3

c: \(y=x\left(x+3\right)\left(x+1\right)\left(x+2\right)\)

\(=\left(x^2+3x\right)\left(x^2+3x+2\right)\)

\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1-1\)

\(=\left(x^2+3x+1\right)^2-1>=-1\)

Dấu'=' xảy ra khi x^2+3x+1=0

hay \(x\in\left\{\dfrac{-3+\sqrt{5}}{2};\dfrac{-3-\sqrt{5}}{2}\right\}\)